Periodic downtime

Every so often my linode (which hosts a low traffic Rails app) will not respond to web requests for a few minutes. I just get a timeout. I have started seeing a pattern, where this will happen at a particular time each week. This doesn't correspond with any cron jobs I have set up.

I've checked my logs and see regular attempts to SSH into my linode around the same time that the linode becomes unresponsive. I've installed fail2ban, which is doing its job, but my understanding is that these attempts wouldn't be enough to cause a bottleneck.

My graphs are good - CPU average of ~4%, and I/O rate average 6.55.

Is there something else I should be looking for here? Or another way I can diagnose this issue?

Thanks!