What that book says
This reader totally agrees that when the description of the magic weapon special ability spellblade (Player's Guide to Faerûn (Mar. 2004) 141) (6,000 gp; 0 lbs.) says, "When the wielder is next subjected to the chosen spell, the weapon absorbs it," that description is being incredibly unclear and that it's unclear no matter how it's translated.
Really, the DM can rule that it means anything from the renders-the-ability-pointless When the wielder is first subjected to the chosen spell, the weapon absorbs it, and, after the spell drains harmlessly away or is directed at a new target, the magic weapon special ability spellblade is forevermore gone to the let's-add-some-words When the wielder is first subjected to the chosen spell each round, the weapon absorbs it to the potentially-overpowered Whenever the wielder is subjected to the chosen spell, the weapon absorbs it—full stop. There's no erratum—anywhere—for the magic weapon special ability spellblade, so going exclusively by the words in the Player's Guide, if the DM allows such an ambiguous ability into the campaign in the first place, the ability spellblade works the way the DM rules it works.
However, before making any ruling, a DM should know that until the Player's Guide—so for over a decade—there was no question as to how a spellblade works.
What other books say
Originally appearing in Ruins of Undermountain (1991) for Advanced Dungeons & Dragons, Second Edition, the final version of that edition's spellblade (Encyclopedia Magica (1999) 1,404)—that's largely identical to Undermountain's description—is a +2 magic weapon that also says
A single wizard spell is cast as part of its making, and after that the sword is immune to and paramount over that particular spell. Anyone carrying a spellblade who is attacked by the particular spell that the blade is linked to is utterly protected against all of that spell's effects. This immunity applies even if the spell is [like magic missile an] 'unerring' spell, [sic] or one that a weapon would normally be of no use against.… There is no known limit to the negation ability of a spellblade against its specific spell.…
This description begins with some lore about how only recently have spellblades come back into fashion, probably from a source in Sembia, and the description ends by saying, "Most spellblades are crafted to protect against offensive spells…; a rare few are made for specific purposes, [sic] and can breach prismatic spheres or walls of force."
A creature in Second Edition that opts to keep the spellblade gains 1,000 experience points plus 100 experience points per level of the spell the spellblade negates. If the creature instead sells the spellblade, he receives 6,000 gp plus 2,000 gp per level level of the spell the spellblade negates. For comparison, in Second Edition a luck blade (1,381) that grants a +1 bonus on saving throws and that has 1d4+1 wishes remaining but that number is a secret from the wielder is worth 1,000 experience points if kept and 5,000 gp if sold, and a sword that's vorpal (called vorpal II on 1,412)—a +3 magic weapon that sometimes lops off a foe's head—is worth 8,000 experience points if kept and 40,000 gp if sold. This would seem to put a high-spell-level spellblade—one that could, in Second Edition, allow its wielder to walk unimpeded and unharmed through a prismatic sphere, for example,—in the upper-middle of magic weapon values.
I bring this up because Third Edition is largely reluctant to slaughter sacred cows, often preserving at least its earlier editions' game elements' spirits, and the spellblade is no exception. So while the kinds of spells that a spellblade could be "paramount over" changed substantially in Dungeons & Dragons, Third Edition, remaining unchanged is the spellblade's basic idea: the weapon allows the wielder to ignore and hurl back a specific spell… repeatedly. That is, the initial Third Edition version of the magic weapon special ability spellblade (Magic of Faerûn (Aug. 2001) 141) (+1 bonus; 0 lbs.) says
The wielder is immune to a single spell chosen at the time the weapon is created. The chosen spell must be one that is targeted against the wielder (not a spell that affects an area). When the wielder is subjected to the spell, the weapon absorbs the spell. On the wielder’s next turn, she can opt to let the spell drain harmlessly away or direct the spell at a new target as a free action.
So it's not until Dungeons & Dragons 3.5 that questions could be raised about whether or not the magic weapon special ability spellblade is reusable. That is, the complete description of the revised magic weapon special ability spellblade—an excerpt from which opens this answer—says
The wielder of a spellblade weapon is immune to a single spell chosen at the time the weapon is created. The selected spell must be one that is targeted against the wielder, not one that affects an area or creates an effect. When the wielder is next subjected to the chosen spell, the weapon absorbs it. On his next turn, he can opt to either let the spell drain harmlessly away or direct it at a new target as a free action. (PG 141)
Thus if the DM rules that the lone word next in the 3.5 description of the magic weapon special ability spellblade means that the magic weapon special ability spellblade is usable but once then the magic empowering the spellblade is gone, that DM is going against the longstanding published history of the spellblade. That's not a criticism, by the way! A DM can totally do that based on the Player's Guide description! But a DM should also be aware that he's doing that.
"Maybe it's clarified elsewhere?"
My search of the majority of Third Edition and 3.5 treeware and the Wizards of the Coast Web site turns up only two creatures actually employing a magic weapon with the magic weapon special ability spellblade: Alauneth "Black Viper" Orrane (City of Splendors: Waterdeep (June 2005) 69–70) who wields a +1 spellblade rapier keyed to the spell magic missile and Kaanyr Vhok (Power of Faerûn (Mar. 2006) 130) who wields a +2 spellblade longsword keyed to the spell cone of cold, a spell, by the way, that in this edition can't usually be keyed to a spellblade. Of course, neither description mentions the creature expending the spellblade ability.
Champions of Valor (Nov. 2005) on the prestige class knight of the Weave on Resources mentions in passing the spellblade magic weapon special ability, saying that a knights' favorite magic weapon special abilities are "the speed, spellbladeMag, and spell storing special abilities (as well as dispellingMag weapons for knights who don’t have the ability to cast dispel magic)" (114). Likewise, this description doesn't mention if the spellblade ability expended after its used.
What I did find interesting is that even though all three of Waterdeep, Power, and Valor were published after the Player's Guide, only Power references the magic weapon special ability spellblade from the Player's Guide to Faerûn (and, as noted, applies it wrongly). The other two texts reference the initial Magic of Faerûn version (hence, for example, the superscript Mags in the above quotation). I refuse to draw a conclusion from what certainly could be simple editorial oversights, but readers should be aware that, long after the revised version's publication, redirects to the initial version occurred more often than redirects to revised version, which is, even by Wizards of the Coast's standards, pretty weird.
And, just to be clear, this DM does allow the magic weapon special ability spellblade to function any number of times as per its Magic description but otherwise uses the updated information from the Player's Guide.
Note: I've another 500 or so words queued up addressing possible issues with the spellblade ability, but I've omitted that section since this answer already runs long, and that opinion is—possibly—beyond this question's scope. In sum, though, while this other fine answer recommends banning the ability, my experience has been that the spellblade ability when keyed (inevitably) to dispel magic et al. is as much burden as benefit. Please pose a separate question along the lines of What's the long-term campaign impact of allowing creatures to use the magic weapon special ability spellblade keyed to the dispel magic spell and similar spells? if interested in answers to such a question.