So I used to be that guy who wanted to serve all the time. I used to have to scream to use my talents. I was new to the church with many years experience doing audio than even the "full-timers" had. When I wasn't asked to serve, I actually would think that it was because they didn't want me or there was some kind of personality conflict causing a sort of rift in their passing me by.
Flash forward a year or so later. I'm deeply involved with other ministries in the church. Some of which taken on because I wasn't being scheduled enough in audio. We hit a dry season... summer. A good portion of our congregation
loa array and volunteers are college students. During the summer, many go back home for a few months or take on full-time jobs that aren't very flexible with hours. So leadership began scheduling me more and more while I was stretching myself thin. My early requests began to come back to haunt me. I began suffering from burnout which would result in lower performance in the one area where I had the most experience outside the walls of the church.
That being said... I say schedule them for as much as they feel that they can handle. Willing volunteers are a rare gem and it's been my experience that there's really an ebb and flow of good volunteers available. One month you're booked solid with possible backups on standby. Other months, you're having to cover multiple slots at multiple times. The important thing is treat this gem of a volunteer with care. If you notice signs of breakdown, allow them to take a break. Give them time to experience what you guys do together from the viewpoint of the spectator.