The problem still happens, but I noticed it's not at exactly the same time (but close) and it doesn't happen every day.
It's hard to be on an edge switch to gather traffic because I don't know which one will go down at exactly when. I have 2 IPs on each switch, but both IPs drop so I can't log in remotely. They are a little bit far from each other so I would have to run between them, log into the console locally, and run these commands while the problem is happening.
I'm wondering if it is someone doing network scanning and this causes increased broadcast activity and maybe there is some threshold in my EX4500 VC aggregation switch that I don't know about. I don't have one configured.
I'm not that knowledgeable about Juniper hardware (yet).