[exim] Connection refused: too many connections - why?

Hello,

after few days running flawlessly, exim suddenly decides to fail.

I then find hundreds of
Connection from [some address] refused: too many connections
in the log file and 20 instances of exim running but idling. I've to
stop the main exim and kill all instances one by one.

The server is under almost no traffic, so the server isn't overloaded.
And the log also doesn't show connection attempts right before the error
lines start.

What could that be?

Jürgen