If you can’t change your DHCP pool, can you reserve the IP you want for the device in the router? You should be able to at least do that. That doesn’t answer the question as to why you are having problems, but it will get you going, and if you can’t change the pool, will prevent the router trying to assign something else to that ip. If you reserve in your router, be sure to change the setting back to DHCP in your windows device. Sounds like either another device is picking up that IP or your settings are off. If you want to stick with setting on your device, have you tried retyping everything in the network settings? What I mean is, completely delete every field, ip, subnet, gateway, dns, and retype. Verify it’s accurate. Then open cmd as admin, then release/renew and reboot or at least flush dns. It’s pretty easy for your brain to overlook an incorrect setting, when it wants to see the correct one. Happens to me all the time, lol.
Is the router wireless too? If so I would connect my phone to it and when you get an outage on a computer, check if your wifi is working. If it is, it’s something in the hardwired components. But if the Internet connection drops on wifi too, you know it’s somewhere in the router or past that to the external network. Have you power cycled your network equipment? Any chance you have a laptop handy? You can test right at the switch or at the router when your computers drop.This will help narrow down where to look further.