weird connection problem

Hi. We are running a MySQL5.0.24 database on Debian Sarge,2.6.something
kernel. This machine is also used for other occasional disk-intensive
processing, and when those processes starts, MySQL refuses to accept
remote connections. Connecting locally works fine and mysql itself
doesnt seem to suffer too much from the other disk-intensive processing
going on. The database is a small one, used by around 20 people that
uses it a couple of times per day, so the load the database imposes on
the machine is very low.
When this happens (clients doesnt get connected...) there is no messages
anywhere in any logs. Doing strace on the mysql process combined with
tcpdump, shows that it sees the remote connection, sends an ack or
something, then it doesnt send anything more, at all. Connecting locally
still works fine though, even using -h localhost.
Connection to this machine using ssh or other methods remotely during
the high-processing works fine, its just MySQL that refuses to accept
remote connections.
Anyone else who has experienced this kind of behaviour ?

Any ideas are very much welcome, we're starting to run out of them
ourselves :-) Thanx

/zw