I found a bug in the AppKeepAlive which may be/probably is the cause of this, though I have not been able to cause a hang in my dev environment this bug could theoretically be the culprit. I don't think those errors logged by the feed manager are the cause.
The problem I found (and have now fixed in my copy for the next release) is that multiple instances of the AppKeepAlive task could be spawned. I have added logic to check if another instance is already running and then end the new instance immediately after it is started if so.
If you look in Administration > Advanced Tools > TaskQueue and you see a AppKeepAlive task running then you touch web.config to recycle the app, you'll see 2 of them, do it again and you'll see 3, and so on. So theoretically it could just keep going and exhaust the thread pool and this would cause the site to hang.
I will try to get a release out soon with this fix but in the meantime it may be best to keep an eye on the taskqueu and if you see a bunch of AppKeepAlive tasks it may be best to disable that for now.