It's often people who have a hard time saying no who end up spread thin over a number of gigs - this leads to burn out. Or not showing up to meetings... The 3/5 of the board who can't be rounded up are also signed up for too many things.
When I was chair of a small non-profit (currently still a board member after a hiatus for a few years), I'm not sure I'd have described it as burnout but increased lack of engagement and interest definitely became a problem over time. When we did require in-person votes/quorums, that did become a problem because it usually required traveling for most board members 2 or 3 weekends a year.
At some point, while I was on hiatus, the board did change its rules to allow telephone and, later, Zoom attendance which has been IMO something of a mixed bag but probably inevitable especially post-COVID. I'd like people to get together in person more but it's harder than when the board skewed younger; people have more family responsibilities at this point and, of course at this point, a lot of people just have less patience about getting together physically when business can mostly be taken care of over a couple hour Zoom call.
Fortunately, the non-profit's regular activities and finances have been on a pretty even keel so the board mostly just keeps an eye out for problems.
