Why do close votes expire? And if they do, why does Area 51 not allow those who had voted previously to vote again to close?
The data for close voting on Area 51 proposals is a little hard to track down. But from my experience, the vast majority of proposals are abandoned and deleted after 30 days of inactivity. Quite a few proposals are closed within a few days with the help of a moderator. (Basically Robert or another employee.) It's not uncommon for proposals to be closed by the community within a week or so. So what's at issue is close votes that expire on proposals that have legs.
Of the proposals that don't get closed early and aren't abandoned, nearly all fail to drum up enough support before the deadline. It's hard to gather the right group of people to make a site work, so the barriers are somewhat high. Getting a site near the launch threshold requires significant total cost. Many people have worked together to create and vote on example questions. In most cases, there have been numerous discussion posts written. People have invited others to commit. If the proposal might become a viable site, we want to strike while the iron is hot.
I don't really know if Area 51 was designed this way or if it's a happy accident: aging out close votes prevents a few people from negating the work of a great many of others at the eleventh hour. If a proposal is to be closed, it really needs to be done early—before people have wasted a lot of time. Don't forget that the main purpose of Area 51 is to vet site proposals to improve the odds they will become a viable community. The further a proposal gets in the Area 51 process, the more likely it is to succeed as a site.
One final thing to remember: the Community Managers review every proposal that nears 50% commitment. We do sometimes close proposals deep in commitment, but we don't take this decision lightly. One of us usually takes on the task of explaining exactly why we are closing the proposal. It's unlikely that someone casting the fifth and deciding vote would do the same.