I think the biggest challenge to me being the sole DBA is going to be this year, though, in August, when I'm taking a 2 week vacation and travelling down south. I don't plan to take my work laptop along, although I may take my work phone along, it'll spend 99% of the trip in the room safe only occasionally getting pulled out for me to check e-mail. I'll do my level best in the months between now and then to get everything in order so that best case when I get back I'll just have to catch up on a stack of e-mails, but there's always going to be the unexpected...
Good luck with getting away. I've been in that situation, and for smaller organizations, it's a challenge to have a backup. Usually I try to doc things and get another person involved and teach them rudimentary solutions to things I know commonly occur.
Outside of that, until there's a problem, likely management won't do more.