This is no different than a mod-closure. If the question gets closed all pending close votes are consumed. A tag-badge closer is really just a highly-localized moderator in this case (duplicates only, in specific tags only). For that matter, it's the same as a community closure -- but with the reopen requiring more people, which seems to be part of your point here.
In all closures, reasons that aren't the one that ultimately "won" get lost along the way along with their votes. If two people vote "too broad" and three vote "unclear", "unclear" wins and the "too broad" reason drops out. The votes contributed to the closure, but not for that reason.
Yes it's frustrating -- once you've voted to close a question you can never, ever vote to close it again, no matter what happens to it in the meantime, so if you voted to close and it got reopened (perhaps with edits you deem insufficient to fix the problem), there's nothing you can do directly. This is true no matter how the question got closed or what specific votes were cast.
Perhaps what you are looking for is an "oops" button -- I'm a mod or badge-holder and just unilaterally closed that and then realized I shouldn't have. This would mean retracting a close vote that has already taken effect. This would add complexity to the interface and confuse some people, so I doubt it would be considered without more evidence that this is a problem, but that's the approach I would take if I wanted to pursue a change here.
Alternatively, if the problem is that your vote is locked once consumed, attack that aspect (applying it to all closures). I expect that this has come up on MSE before.
Finally, remember that if you can't recast your own close vote, you still have meta and chat as tools to encourage others to vote.