Yes, you can meet requirements with magic items
Simply stated, anything at all that results in you having the appropriate stats, skills, features, and so on, will meet a requirement for feat or prestige class. The game makes no distinction, at any point in the rules, for how your stats got to be the way they are; it only cares what they are.
To back up this claim, first some
Definitions
Below are the sum total of relevant rules, which define what requirements are.
Player’s Handbook pg. 87
Chapter Five: Feats
Prerequisites
Some feats have prerequisites. Your character must have the
indicated ability score, class feature, feat, skill, base attack bonus,
or other quality designated in order to select or use that feat.
Dungeon Master’s Guide pg. 176
Chapter Six: Characters
Prestige Classes
Unlike the basic classes found in the Player’s Handbook, characters must meet requirements before they can take their first level of a prestige class. [...] If a character does not meet the requirements for a prestige class before that first step [of leveling up], that character cannot take the first level of that prestige class.
These are the only rules about requirements in the core books. Furthermore, per the errata rules,
Errata Rule: Primary Sources
When you find a disagreement between two D&D® rules sources, unless an official errata file says otherwise, the primary source is correct.
The Player’s Handbook, for example, gives all the rules [...] for using base class descriptions. If you find something on one of those topics from [other D&D® rules sources] that disagrees with the Player’s Handbook, you should assume the Player’s Handbook is the primary source.
Prestige classes are not explicitly listed as being one of the topics for which the Dungeon Master’s Guide is the primary source, but the fact that the list for Player’s Handbook explicitly says base classes, and that prestige classes are found in the DMG to begin with, makes that pretty clear. So no other rules source should be considered to answer this question.
Notably, that includes a sidebar in both Complete Arcane and Complete Warrior that directly address this topic (but then add rules that fail when applied to one of the DMG prestige classes, making the entire sidebar suspect, even barring the technical application of the errata rules). It is worth keeping in mind, however, that a sidebar included in the very first two 3.5 supplements support the notion of meeting requirements with temporary effects.
So these two rules quotes are the entirety of what we have to go on. They say only that a character must “have” or “meet” the indicated requirement, with no indication given that there is any special rules for how to determine whether or not a character does.
Do bonuses count? Yes, yes they do
So, do bonuses count towards “having” or “meeting” some numerical requirement?
Player’s Handbook pg. 10
Chapter One: Abilities
Changing Ability Scores
Over time, the ability scores your character starts with can change. Ability scores can increase with no limit. Points at which ability changes occur include the following:
Add 1 point to any score upon attaining 4th level and at every
fourth level your character attains thereafter (8th, 12th, 16th, and
20th level).
Many spells and magical effects temporarily increase or decrease
ability scores. The ray of enfeeblement spell reduces a creature’s
Strength, and the bull’s strength spell increases it.
Several magic items improve ability scores as long as the character
is using them. For example, gloves of dexterity improve the wearer’s
Dexterity score. (Magic items are described in the Dungeon
Master’s Guide.) Note that a magic item of this type can’t change an
ability score by more than +6.
All of these things are being treated equivalently under the rules, even the +1 bump every four levels. No distinction is made, in terms of what your score is, between permanent and temporary bonuses – even very temporary bonuses like spells. When a bonus or penalty is applied, that changes what your score is, and that changes whether or not you meet a requirement.
The Player’s Handbook even has an example: a negative one, but nothing says that this is a special case for penalties that doesn’t apply to bonuses:
A character can’t use a feat if he or she has lost a prerequisite.
For example, if your character’s Strength drops below 13
because a ray of enfeeblement spell, he or she can’t use the Power
Attack feat until the prerequisite is once again met.
Requirements for base values do exist, of course
There are three defined categories of base values: base attack bonus, base save bonus, both defined on page 22 of Player’s Handbook, and skill ranks, defined on pages 61 and 62 of the same. These things are frequently used in requirements, and generally cannot receive permanent bonuses.1
Note, however, that the rules never define an analogous “base ability score” term. There is no way, under the rules, to refer to such a thing (and ultimately, it’s unclear what that would be). Thus, as far as the rules are concerned, your ability score for the purposes of requirements is your ability score in general, the one used for all other purposes.
Timing of level-ups and temporary bonuses
Player’s Handbook and Dungeon Master’s Guide are intentionally vague about the in-character process of leveling up; levels are, after all, an abstraction, and the narrative that goes with them depends on the table and game.
Player’s Handbook pg. 58
Chapter Three: Classes
Experience and Levels
When a character earns enough XP, he or
she attains a new character level (see Table 3–2: Experience and
Level-Dependent Benefits, page 22).
Advancing a Level: When your character’s XP total reaches at
least the minimum XP needed for a new character level (see Table
3–2), he or she “goes up a level.”
Dungeon Master’s Guide pg. 197
Chapter Six: Characters
How PCs Improve
The rules in the Player’s Handbookassume that characters have access
to everything they need to advance in level—libraries where they
can research new spells, trainers to guide their efforts, and places to
practice new skills and abilities. Research and training aren’t a part
of the standard rules. They’re assumed to be going on in the back-
ground. However, you control the background and can decide how
you want to handle things such as this. Keep in mind, however, that
leaving them in the background is a fine choice.
(emphasis mine)
Dungeon Master’s Guide then goes on to describe optional things a DM may do, or require, for a character to gain the benefits of leveling up as described in Player’s Handbook, but none of these are default (and as the bolded section indicates, Wizards does seem to favor not getting too detailed in this area). The Player’s Handbook is even more hand-wavey, stating simply that as soon as your character gains sufficient XP, ding!, he or she “goes up a level.”
So what happens if your character happens to go up a level while under the effect of a spell that provides a bonus or penalty? All the rules above would have that effect change whether or not the character qualifies for feats or prestige classes. A feat gained in this way would be unusable without the effect, since the requirements for feats are there both for gaining and for using them, but prestige classes don’t have the same rule (the aforementioned sidebar in Complete Arcane and Complete Warrior attempt to add it in, but that works very poorly in the case of the dragon disciple in Dungeon Master’s Guide).
Most DMs won’t, and shouldn’t, allow that, and the rules are more than vague enough that it wouldn’t even really be a “houserule.” The DM could just award XP, say, overnight, rather than immediately after a challenge is completed (when temporary bonuses and penalties may still linger). Player shenanigans can get around that too, but that comes up against the general social expectations of playing the game; that sort of behavior is not acceptable at many tables, rules-allowed or not.
Alternatively, even a DM not using some of the optional ideas presented in Dungeon Master’s Guide for requiring training and research, could easily state that while these issues are generally left in the background, the specific case in question (a given bonus or penalty applied) the lack of training with that temporary effect means that you go up in level as if it weren’t there.
But magic items are rather persistent. Presumably someone could be training or researching while taking advantage of them. This makes it harder to justify eliminating them, and ultimately, the game rules allow their use for this purpose.
About the FAQ
The FAQ, sadly, has enough flaws that it is generally not seen as an authoritative and credible source. The errata rules make it clear that, as far as the rules as written are concerned, statements made in the FAQ are meaningless unless they are backed up by the published rules.
So here’s what the FAQ has to say:
A feat sometimes requires you to have a certain ability score, which is the case with Two-Weapon Fighting (it requires Dex 15). A character has, say, Dex 13, but wears an item, in this case gloves of Dexterity +2, and now her Dex score is 15. Can she take the feat and have it be active only when she wears the item?
Actually yes, she could take the feat, but she would lose the use of the feat if, for whatever reason, she loses the bonus from the item.
Per my the rest of my answer above, this statement is backed up by the published rules! That means this statement is valid, and while this statement isn’t true because it was written in the FAQ, it is true. This is, perhaps, the FAQ at its best: players have an intuitive sense that there might be a distinction between temporary and permanent bonuses, when it comes to requirements, and though the topic is effectively covered in full by the published rules, it requires the synthesis of numerous definitions across several books to determine that fact. The FAQ provides a nice, straight-forward, explicit answer, that is accurate if you go back to the official rules. If more of the FAQ was as good and useful as this answer, it would have a much better reputation than it does.
No item grants a continuous improvement to any of these values.
A few spells (most notably the cleric spell divine power) temporarily improve base attack bonus, but nothing that last a significant amount of time (...until Persistent Spell comes into play).
As far as I know, no effect in the game improves base save bonus.
For skill ranks, the one and only option (barring shenanigans typically involving psychic reformation or similar) is the Primary Contact feat in Cityscape, which gives you a single extra rank in one skill the level you take it (thus allowing you to surpass your maximum on that level).
