Just and update for information purposes. We finally found the source of the problem, which was not WordPress related at all. Due a large amount of spam mail sent to our server (some 15,000 a day!!!) the number of processes going on at the same time exceeded the limit given by our host. Hence WordPress just timed out. We have now reconfigured the mail server to reject emails going to generated addresses that are not defined by us. This seems to work.
Thank you very much for the response. We are using Verio Virtual Private Servers we believed this solution to be good enough, but it clearly is not. I will take the liberty of quoting you in mai correspondence with them!
Per Koch
We are facing the same problem. From time to time WordPress fails in generating pages and gives ut the message above instead. Could this be caused by overload? Too many visitors? Search engine spiders? And if so: Is there anything that can be done to alleviate the problem?