The practical limit to the number of containers you can run on one system is in the high hundreds or more thousands, depending on how you configure some things, and your available hardware. It's certainly more than you'll even use unless you get into some auto-scaling swarm config stuff.
The issue is more about resource limits, and access to shared resources. I'd start by trying to figure out if there are certain specific containers that don't play well together. Bring your setup online slowly, one container at a time, and take note of when things start to get funky. Then start testing combinations of those specific containers. See if there's one you can remove from the mix that suddenly makes things more stable.