I thought the community deserved a little update on the internal moderator discussions on this point. My answer below just speaks for me, but I did run it by the other moderators, and got no objections. It's my attempt to lay out our thinking, so that people have a chance to disagree.
Our basic calculation is that moderator elections have the potential to create problems and there don't seem to be any issues they are likely to solve, so until we see a change in that balance, it doesn't make sense to elect new ones. None of us are strongly opposed to moderator elections, now or on general principle, but at the moment, we've agreed that the (small) risks outweigh the (small) benefits.
Let me talk about both sides of that equation: I don't think I need to point out to anyone who reads the news that elections can have unpredictable consequences. I think it's pretty unlikely that the MO community would elect someone who created any serious issues or who had big clashes with current moderators, but life is unpredictable. I think this is a little trickier with MathOverflow than it would be with another StackExchange site because of our unusual history and identity within the StackExchange network. As Gerhard mentioned, there is a separate non-profit run by the moderators which exists mainly to hold onto our option to go independent of the larger StackExchange world if the need ever arose; it also exists to accept funds which could potentially be used against future costs (ironically, the main thing we have actually used money for is to set up the LLC; this was done with a grant from the Sloan Foundation). Again, I don't think that the MO community would elect someone who didn't appreciate the site's mission and what makes it different, but a moderator election would raise some sticky questions (would we commit to adding the new moderator to the board before the election?) that seem like unnecessary complications.
The opposite side of this is the potential benefits. I think that this question started with the observation that several of the moderators are not especially active. This is undoubtedly true, but largely stems from the fact that Todd tends to get to moderation flags before any of the rest of us have a chance to see them. The number of questions requiring by hand moderator intervention is quite small (and most them don't actually require it); if you look in data explorer, you'll see Todd took almost all the by-hand actions in the last year, but that the total number (not counting Community) is around 50, so one a week. Actually, becoming a moderator can interfere with participating in day-to-day moderation, since voting for closure or deletion as a "civilian" is impossible and your vote on its own will close or delete a question. I think arguably the last few years proves that Todd could handle the day-to-day moderation on his own if he needed to (not that we would ask him to).
So, the much more important thing moderators do is deal with occasional weird and difficult cases (we occasionally have banned users who very stubbornly try to post under different accounts, vote fraud, etc.) and act as long term stewards of the site. We do also have the bully pulpit to weigh in on issues facing the site, though that's only really our moral suasion (and electing a new moderator wouldn't do much to give them more authority on this point). If that or some other aspect of the moderator job needs new blood, I think the current moderation team is quite open to having elections, but I haven't seen a strong argument for it.
