Since I started it, I thought I ought to finish it....

I believe I have figured out the problem. I use an Exchange server to take advantage of the DirectPush mail on my 8125. It seems that DirectPush stuff was trying to initiate a connection while I had the N770 tethered. This was halting the data on the N770. I discovered that if I temporarily disable DirectPush on the 8125, that then the N770 1) almost always connects on the very first attempt, and 2) does not appear to drop the connection.

So, anyone trying to tether using a WindowsMobile device with DirectPush mail, you might want to go into the connections manager and disable DirectPush while you're trying to do a tethering session on the N770/N800.