Humans gain an extra skill point per level from their 'skilled' racial trait. If I become a human after first level (via reincarnate, polymorph any object, becoming a mythic creature, or some other method), do I gain retroactive skill points as if I had been human for each of my levels? Similarly, if I lose access to my 'skilled' racial trait as a human do I lose a skill point per hit die? Why?
in D&D 3.5 this would definitely not be the case. There were no retroactive calculation of skill points, even if you spent an attribute increase on Int.
But for pathfinder it is different.
All bonuses are retroactive when an ability score increases, be they bonuses to damage, to skill ranks, to hit points, to saves, to skill checks... all of them. Skill ranks not being retroactive are a 3.5 convention we specifically removed from the game because it was a weird exception to the rule, and since now there are no exceptions to this rule, there's no need to specifically state that skill ranks are retroactively granted if your Intelligence goes up.
Given, he was talking about Int increases. But since they already concede that skill calculations are retroactive, there is no reason to believe the human racial modifier is not included.
Just this is so rare a case that was not mentioned.
An honorable mention to David Wilkins for posting this up on a related question.
Strictly speaking, this isn't an ability score increase, rather a racial type change, which I do not believe is addressed specifically in the rules. However, Adding Racial Hit Dice, Step 4: Skills and Feats mentions
When adding skills, check to see if the creature's Int modifier changed. If it is unchanged, simply multiply the total number of ranks per Hit Dice gained by a monster of its type times the total number of added Hit Dice and add that number of ranks to its existing skills. If its Intelligence modifier has increased, perform the same calculation as if it had not increased and then multiply the change in its Intelligence modifier times its new total number of Hit Dice and add that number of additional ranks as well (adding new skills as needed to spend all of the ranks).
And clearly here, the intent is to retroactively add the new skill ranks, like with an ability score increase.
The reasoning for Pathfinder doing this different than 3.5 is simply that Int was a weird exception. However, more important to running the game; additional bookkeeping is required without retroactive adjustments. That is, you have to keep track of when each adjustment is made to accurately determine skill ranks and this history is not normally a part of any stat block.
I think this is why many 3.5 DMs house-rule retroactive skills.
TLDR: Because the "Skilled" feature in the Human Racial Traits is not a physical feature, it is neither gained nor lost by magical effects such as Polymorph Any Object, or Reincarnation that change your race, since these effects specifically do not change the mind of the targeted creature.
The Reincarnation Spell in Pathfinder reads:
A reincarnated creature recalls the majority of its former life and form. It retains any class abilities, feats, or skill ranks it formerly possessed. Its class, base attack bonus, base save bonuses, and hit points are unchanged. Strength, Dexterity, and Constitution scores depend partly on the new body. First eliminate the subject’s racial adjustments (since it is no longer necessarily of his previous race) and then apply the adjustments found below to its remaining ability scores. ... The reincarnated creature gains all abilities associated with its new form, including forms of movement and speeds, natural armor, natural attacks, extraordinary abilities, and the like, but it doesn’t automatically speak the language of the new form.
All specific examples of abilities gained from the new form in the Reincarnate spell are due to changes your physical form, you only gain those racial abilities and traits that are associated with the new form's physical body. Similarly, you only lose those racial abilities and traits that are associated with your old form's physical body. That is why your Strength, Dexterity, and Charisma may change, but your Intelligence, Wisdom, and Charisma do not change, even if your new form would normally get a bonus or negative to a mental ability score. So from a RAW perspective, no, you would not gain or lose skill points based on becoming human or transforming from human into something else.
I also contend that the RAI and a good sense of verisimilitude in the game also require that your skill points remain unchanged by effects that change only your physicality, such as the Reincarnation spell.
The extra skill points in question are a cultural benefit from being raised as a human and are intended to represent the diversity of human culture. Similarly, you would not acquire a bonus feat because you were reincarnated as a human.
Finally, it only makes sense that you would retain any cultural abilities from your previous form, such as racial spellcasting, or weapon training, since those are things that you already learned and are not erased from your memory.
In the case of Polymorph spells:
In Pathfinder, Polymorph is an entire family of spells that encompass everything from Alter Self to Form of the Dragon, all of which offer mostly lesser benefits of being the type of creature you turn into, rather than fundamentally changing every aspect of the target. In most cases it modifies a few of your physical ability scores, your sensory abilities, and movement abilities, such as flying, burrowing, swimming, etc. The Spell you specifically cite in your question, Polymorph Any Object, states that it works like Greater Polymorph (which directs you to various forms of transformation spells listed above) except that you can turn anything into anything else. It does not, however, say that it alters the mind of a sentient creature that is targeted, rather it can grant sentience to a non-sentient object turned into a sentient creature.
Baleful Polymorph is the only one I know of that specifies that it changes the mental state of the target:
The creature loses its extraordinary, supernatural, and spell-like abilities, loses its ability to cast spells (if it had the ability), and gains the alignment, special abilities, and Intelligence, Wisdom, and Charisma scores of its new form in place of its own.
Even in this case, however:
It still retains its class and level (or HD), as well as all benefits deriving therefrom (such as base attack bonus, base save bonuses, and hit points). It retains any class features (other than spellcasting) that aren’t extraordinary, supernatural, or spell-like abilities.
Racial abilities other than spellcasting training are not specifically addressed, but it can be assumed that such things as skill points, feats, weapon training and the like would remain unchanged, and, assuming the anatomy of the new form permits it, available to the subject of the polymorph spell. Additionally, because your question was about Polymorph Any Object rather than Baleful Polymorph, the subject's spellcasting ability and mental ability scores would not be changed. I included Baleful Polymorph to prove a point that even in the most extreme case of shape changing available in the game, your skill points would still remain unchanged by the transformation.