This can be a tricky one. I think sometimes small churches can try and run all sorts of programs that they can't support, although if they run too few programs it's potentially more likely that they'll struggle to retain visitors.
Small churches may suffer with problems relating to very small cliques wielding disproportionate amounts of influence and pushing their own agendas through. At my last church it seemed a very small group became obsessed with live streaming services. We didn't have the volunteers to make it happen and nobody could define exactly what they wanted, but a select few continued to push it. Now, nearly four years later, there's exactly zero progress but the last I heard it was continually resurfacing. Before I left I saw no evidence that anybody except for a couple of people cared about it but it kept coming back like a bad penny.
Youth ministry can be very difficult in a small church. If there's going to be any form of sharing the load you need different people to teach kids every week and you don't need much diversity in ages before you need multiple groups. If you have three kids in the entire church but they are aged 2, 8 and 14 it's not going to work well to put them all in a single "children's class" but you potentially need 12 volunteers to cover three classes every week.
It's also good to just let people serve. In some roles there might be particular standards that need to be met but beyond that when you're really short on volunteers it's not a smart idea to annoy them or overload them. People will put up with a lot of aggravation but once they hit a certain point they'll just walk away. A friend of mine served his church in multiple ways until he got burned out and quit everything. I served in multiple places before I got sick of a variety of things, at which point I resigned from everything at once and stepped away. So the church, which wasn't exactly swimming in volunteers before, suddenly had a load of new gaps in the coverage.
Whatever the size of the church it's critical to let people rest and take a break from stuff. Sadly in a few places I've heard church leadership endlessly spout variations of how "we're a family here" and "we're doing God's work so don't slack off" or similar. When people feel the need to step back to recharge, even if only to take a break from something so they can resume refreshed later, it's more likely that they will burn out and quit completely. It's pretty sad when church leaders sound more like cult leaders, drive people ever-harder, and then act surprised when they decide to walk away completely. Likewise if the same person is constantly called on again and again it rapidly drains their goodwill - I personally know a guy who quit serving his church because he was retired and got sick of being the one person endlessly called to help with anything midweek. He was the only one who could do it - as the other volunteers were at work - but once he'd hit his limit he stood down completely.
I suspect in small churches there's the added issue that if you agree to do something you could potentially end up stuck with it for a long time, especially if it requires particular expertise. Once you've started doing something it's harder to stand down when it's clear there's no successor, so it's often safer not to volunteer in the first place.
