Thanks for the tip on ipmonitor. It looks like a nice application.
I found a quick-n-dirty solution for now, a simple perl script that I run from cron. It will check every 5 minutes and send an e-mail if it can't make an http connection to the remote server:
http://stein.cshl.org/~lstein/talks/..._remote_server
For the longterm fix I'm leaning towards trying out nagios (
http://www.nagios.org/) once I find an afternoon of quiet time to devote to getting it installed and configured.