I’m a singing drummer, too (although I’m not the primary singer; I only have two lead vocals in my band’s live set). We’ve got a regular gig at a local bar, playing one night a month and filling in as host of the open mike night when the regular host has a gig elsewhere. We’re lucky in that we’ve become friends with the bartenders who book the shows, so we can reschedule with little difficulty.
Personally, though, I wouldn’t want to sit a gig out if there was any possibility at all I could play. I once missed a gig due to my job. The rest of the band played acoustically, and were horrible from what I heard. But I hated missing the show. I was miserable the whole time.