This evening I've set up keepalived on the two aprs.fi front-end web servers. The program automatically manages the IP addresses of the web service. If one server goes down (due to a hardware failure, operating system or web server software hang, or for a maintenance reboot), the other server will now automatically bring up the service IP address of the first one. The fail-over happens within seconds.
The very same VRRP method is used by the routers serving the hosting network to keep the .1 default gateway address available.
There haven't been any hardware problems so far which would have made this necessary, but now I don't have to go through so much reconfiguration every time I want to reboot a server for a kernel upgrade, or take one down to add some memory. I can also shut down the web server processes on one of the servers (for a more complicated reconfiguration) and keepalived will quickly point all users to the other servers.