What would cause an intermittent cranking problem on a 97 S10 4.3 Blazer that is fixed by disconnecting then reconnecting the battery?

Be most suspicious of the battery itself or of the terminals.

Battery cables can become corroded inside the coating of the cable and may not be noticable from looking at it this corrison can run all the way to your starter. The cables are a cheap repair that can solve the problem. also your ground wire could be corroded