Well, that could be part of the discussion under Leadership of the group - Positions? Elected? Term? Paid?
In a non-profit board that I served on, the executive committee consisted of the Chair (one-year term), Incoming Chair, Past Chair, Treasurer, and Secretary. The only rotating position was the Chair (and incoming/past), which kept new blood in the main leadership position.
Granted, this is five positions, which is pretty much the entire admin group, but it's a suggestion. I totally agree that we can't have a paid grunt position without someone in a designated leadership position who should also be compensated but who would also have defined responsibilities.