I've installed m0n0wall by writing the hd image to an old PC, and am
experiencing some weird network problems.

After a reboot, the connection works fine for a couple of hours. After
that, it seems impossible to make new connections, and the web interface
becomes unavailable.

I though the traffic shaping might be too much for this old machine, so
I turned that off, but the problem remains - only now it seems that the
connection works for a little longer.

I've used the same machine, with the exact same hardware configuration,
as a FreeBSD firewall, right up until installing m0n0wall on it, so I
doubt that it'd be hardware trouble. (Apart from the fact that it's
working fine for a while after a reboot.)

Any ideas on what my problem might be?

My status page, from soon after a power cycle forced by the mentioned
problem, is on http://stp.ling.uu.se/~bkhl/status.html