Connectivity issues with Comcast

Scoured the webs for an answer but couldn't find one, so I'm posting here.

TLDR: If I have too many machines on my internal network trying to access the outside world, is there any reason that my modem should lose connectivity altogether? I would assume, I would just really long lags and some packet loss. But, it appears that my entire connection to the ISP is completely lost.

My story: I have Comcast as an ISP. I've been having severe trouble maintaining connection to the outside world. I'm confident my internal routing is working fine. Every so often, my connection goes down and I get "Request timeout" or "Destination Net Unreachable" trying to ping 8.8.8.8. It seems to happen around noon time when it does occur, but that might just be a red herring.

I can verify that my internal network is working because I can ping my wireless router at 192.168.1.1 and I can ping the modem itself at 10.1.10.1. But, pinging any external address does not work. Also, when viewing the WAN admin page on the modem, it still has an assigned IP address.

Usually, the problem will just correct itself after a few minutes. Sometimes, I get impatient and power cycle the modem. Sometimes, I break down and call their tech support which ends up taking 30 minutes every time. After some checks the tech will always tell me that everything is working "fine", which is a lie.

Additionally, the tech will tell me that I should upgrade my service because it's only 25mb throughput. I cannot understand how this would solve the issue. If I'm running too many devices trying to get to the outside world, wouldn't I just experience a slow connection? It doesn't make sense that running too many devices would BREAK my connection altogether and I'd have to reboot my modem. When I pose this question to the tech, they kind of shrug their shoulders and dismiss it.

Please correct me if I'm wrong. But, I don't think that upgrading my service is the answer.