I did finally get into that site. Interesting reading, but since I've had the issue again since I made that change I think it's safe to say that MTU is not the source of the problem, although it's probably related.
Two things: first, as far as I can tell, the modem does have a router function built in. The modem software control is extremely limited, though, so I don't expect to find any help there, although I may be wrong.
Second, last night I finally tested the idea of removing the router completely. On its own the modem ran fine all night long and the connection was up when I got up this morning.