Internet Outage while using plex

Hi. I have a problem while using plex on my iMac 2011 21" on mi Apple TV 4 gen. Whenever I try to play something, the internet goes down. And the only thing that makes it come back is to restart the router.
My router is a linksys wrt54g.
I tried everything your support page says. Have you heard of this error before?

Sounds like a router issue.

Isn’t that router quite old ??
Just checked Amazon - Date first available at Amazon.com November 15, 2001.

Time to upgrade methinks!

Yes, I thought the same. So after that I bought the Linksys e2500 but the problem persists

@TobiasRuano said:
Yes, I thought the same. So after that I bought the Linksys e2500 but the problem persists

What i would try first is send your traffic to Apple TV via a switch or your old router in bridge mode. Traffic from IMac to internet a patch lead from switch to Modem router. To me it sounds like NAT issue. Also have you added your Apple tv to the list IP addresses in PMS settings. Try Disable secure Connections as a last guess.