I'm in a big bind here, folks. My client is extremely busy, and lives by her email. She could be a great client for me in the future and refer me to others, but I really need to help her out here first!
Ok back to the originial question... When the connection dies try this trick- right-click on the Outlook System Tray Icon (by the clock) and get Connection Status. That will at least tell you what kind of connection it's using if it still exists. Actually view the Connection Status before it crashes as well. If it's connecting using HTTP/RPC there could be issues there. You might try turning off RPC over HTTP if you can (AKA "Outlook Anywhere" in the Connection tab of Account Settings.
Thanks so much for the idea. I'll look for that.
Weirdly, I spoke with the client the next evening, and she said she'd been having no email problems. I'm not sure why, since at the point I left the only progress I'd made was to get a repeatable failure (open Outlook for 10 minutes, and without fail the connection would die). But perhaps one of the 30+ things I tried on Friday actually worked and just needed a little time to get the kinks ironed out. I don't know, but it's one of those times where I'm going to be happy with the results and not tinker with it at all just to figure out what the cause was

I'll deal with it if it comes back.
Thanks for the help, though. I was a little panicked because this will be an important client for me, and I think she's happy so that's good.