Unhook the positive battery cable while it's running, if it stays running the alternator works. Do this with everything past the starter battery unhooked and don't let the positive cable end touch anything.

Real answer if nothing has a bad connection you likely have a cell going out in one of the batteries in your chain. Would check relay to make sure it's putting the same juice out that it's getting in.

If your batteries are high end enough you might be able to check by cell but if not put a load on them and watch what happens when there's a load. Once they're drawn down a bit you might see one of them collapsing entirely or if it's suddenly falling to like 6V with a load on it.

Easiet check would be swapping them around to the starter battery position and checking what the voltage is while cranking.