I've been looking into these memory problems for some time. At the moment we can normally "adjust" our memory usage to fit so that we don't have problems. It still seems even after some adjustments to this memory usage some users still have problems - where for others it has fully resolved the problem.
It's exactly what Michiel says, the issue is with memory available to PHP. The Help & Support page provides this - 256MB. Increasing physical RAM won't do anything and it's purely this "memory_limit" in PHP of 256MB. However, I'd say this is way more than needed. We only need 8MB minimum so you can see there must be a huge amount in use!
One thing I know will resolve the problem is to deactivate poorly written plugins. There are some that appear to use up large amounts of memory regardless of the fact when we run a backup WordPress doesn't run anything else.
The other thing I've seen is that when a plugin is installed it can register large amounts of options in WordPress and set them as autoload (presumedly to optimise loading of the plugin) - but when uninstalled, these options aren't deleted. Sometimes these options are very very big. So even though the plugin was uninstalled, the options are still loading all the time and using memory.
I'll get a test version produced in next few days and post a link in here, so that you can give it a try. I'll attempt to provide more information on memory on Help & Support and also monitor memory usages during timeouts.
Apologies if 4 days was a long time to get a response from me. I've been away and with the plugin been free/non-profit I don't have any cover. I'm normally on the forum every 2-3 days and jump on sooner for issues like this.