I'm currently engaged in the process of acquiring an absentee ballot for the NH Democratic Primary in February, because by then I'll be back in Hampshire, and I have some thoughts on absentee ballots.
In NH you have to apply for the ballot, and have it mailed to you. I believe that getting it is not guaranteed. That said, the form has a really solid range of valid reasons: out of state is one, but there are also allowances for religious commitment, disability, and -- this one surprised me -- being at work during polling hours.
These are good things, and I hope NH voters who work know about that option. But contrasted with this style, I remember when I volunteered in Maine, which had absentee ballots no questions asked. One of the major strategies that the campaign I worked for used was getting supporters of the legalization of same sex marriage to submit absentee ballots just to get out the vote ahead of time, cutting out the loss of votes from people who care, but not enough to actually vote on a non election year.
I can see theoretical problems with absentee ballots like that: trying to get out a misinformation campaign that locks in votes before people can be correctly informed, but I really think absentee voting should be extremely easy. Inconvenience shouldn't be a reason not to vote -- and the answer to that problem isn't casting moral blame on the non-voters. It's re-arranging the system to get their voices counted.