Which versions are you running?
Take a look at this thread, especially at that IMPORTANT bullet. It talks about v1.2.8/9 screwed up db access. Potentially, v1.2.11 fixed something, but not all. On the other hand it may be that v1.2.7 and before didn’t have that problem.
My understanding is that mysqlite serializes all requests, and if it is either not or poorly indexed, it may be that when one request is struggling with getting data, all the other requests in the queue are timing out. However, we don’t see any errors in the logs to substantiate that.
Maybe you could try to increase debug level to DEBUG, and some related errors will show up?