Yep, getting zero votes when you think you've written a good story is dispiriting. We've all been there and experienced that. But, of course, until voting is over, it's impossible to know how many votes everyone is going to get, and voting early would surely eliminate any angst on a monthly/quarterly basis. So my advice is to vote early before there's any hint that a crappy story might achieve success while your own marvellous entry remains unloved. (Personally, though I usually vote late, I rarely if ever look at the Discussion thread, let alone check the poll, before I vote, so it has the same effect -- I don't know what's been going on or who is getting votes/mentions.)
I'd also agree that enthusiasm is bound to wane if one enters a lot but rarely gets votes. However, surely it's enthusiasm for entering. I find it hard to believe someone would apparently be so traumatised at continually getting no mentions/votes that they can't simply bring themselves to vote, and thereby give pleasure to someone else, but they can carry on subjecting themselves to the ordeal of entering the Challenges and getting those no votes.
If members are distressed at entering often but rarely getting votes, then I'd urge them to ask for feedback in the Improving threads to find out why their stories aren't gelling with readers. It may be that the advice given there and/or some simple writing techniques might help, in which case the problem would be solved. If it is the case that their style of writing simply isn't appreciated here, then the adult way to behave is either to bow out gracefully or to accept that one is writing for oneself and that it comes with a price, namely getting no attention from others, but that it doesn't negate one's commitment to/implicit contract with those others. Otherwise it frankly it sounds to me more like a dog-in-the-mangerish I-won't-vote-for-anyone-because-no one-ever-votes-for-me attitude which is as out of place here as those members who try to vote for themselves.
Basically, it's an issue of fairness. Entering without voting on a regular basis is taking without giving back. Reciprocity is the bedrock of any community, and the Challenges are no exception.
Anyway, thanks, everyone, for feedback on the issue, and for some good ideas, especially for trying to reach non-entrants.