Teenagers! I change the admin / admin password and also the network name and SSID password. This blocks certain members of the house to the Internet. when they could be oh I don't know studying for example! The house rule is if you're rude to Mum you're banned for the rest of the day! Problem is the smart one - turns the modem off - everything reverts to the old settings / wifi passwords - and he's off again! How the bloody hell do I prevent that from happening! I've read some threads - seems to be a problem....surely we can outsmart them!
Turning router off/on or rebooting shouldn't reset anything. More likely, smart one is pressing reset switch.
You could consider physically securing the router, eg. lockable cabinet. Or something to block access to the reset switch. Don't block air circulation.