That the address of the modem's router being 192.168.42.1 is normal. The original phone rep obviously needs a little refresher on this.
With regard to the 5Ghz radio issues, until they send out an update to fix it the only option, other than constantly restarting, is to not use it, and just use the 2.4Ghz radio, or, more likely better, use your own 3rd party router. That's about all that can be done, for now.
As for why a web cam would cause a problem with the modem...that's a head scratcher, at least for me. Perhaps an IP conflict? I don't know.
Have you turned off UPnP? If not, give it a try. I suspect all of your connected devices will still work and your disappearing modem problem should be solved. Note that 5GHz WiFi and UPnP are separate issues; I still have not heard of a fix for the 5G issue.
At the request of @Amanda, I have created a new thread about the Gen5 issues I'm seeing:
I disabled UPnP on the modem this morning. After waiting about 5 minutes I powered up one webcam connected via Wi-Fi 2.4G. SUCCESS! The webcam connected automatically and the modem stayed online. It has been working OK for the past 30 minutes. I will leave just the single webcam connected and see if the modem continues working properly for the next 24 hours. If it does, I will add the remaining webcams one at a time. I will update this thread sometime on Friday. Thanks to everyone who suggested disabling UPnP!!!
My modem received a software update two days ago. So far it seems to have fixed my WiFi issue where it completely goes out. I have not tested turning on UPNP yet. Hopefully that has been addressed in this update too.
Yes, a modem update was rolled out to a few gateways for now, which includes the one dredman is on. This update eliminates the need to disable UPnP. Once the update is rolled out nationwide we will make an announcement.