I had another issue with my Last.fm module the other day, which is why it's currently turned off. I think it happens if the Last.fm feeds are unavailable; causing the module's HTTP requests to time out; which in turn causes the whole of Drupal to time out as it waits for the response; which means my whole site falls over.
I've been using the drupal_http_request() function to run my HTTP requests, but unfortunately you can't adjust its timeout setting. So I dug around in that code, and have submitted a feature request and patch which enables you to customise the timeout when using this function. I then rewrote my module with shorter timeouts when making requests to Last.fm, which seems to do the trick.
Hopefully, if this patch makes it into Drupal, I will be able to release the new version of my module, complete with timeouts, so it won't cripple my site or anyone else's. It also adds a Last.fm recent tracks listing to user profiles (if they've set up their username) and has a block (only for one user - I just put it in for myself, really). It still needs a bit of work, and only handles recent tracks, but it's coming along fine.