Can't vote on posts with an existing vote all of a sudden

[JD Martin]

OK, I have a site problem I can't figure out how to solve. Suddenly, I cannot vote on a post if someone else has already voted on it. I can vote on one with no votes, and I can take my vote away from it, but if at least one person has voted I get nothing. 

I have tried clearing all of my cookies, cache, logging off and on, using a different browser, and using a different computer, all to no avail. Any ideas? 

Edit: Thanks, Russell, have added @Mindy Jensen to this conversation :)