Your router will continue to reboot while you run a Smart Scan/Wi-Fi inspector scan.
In order to solve this, you will need to remove the Wi-Fi Inspector component from Settings > Components.
In rare scenarios, when the WiFi Inspector looks for vulnerabilities and bruteforce attacks the router, some routers reboot. The only way to solve this is by removing the Wi-Fi inspector component for now.
In the future (rather later than sooner), Avast will add advanced options to the Wi-Fi Inspector where you can disable some parameters in order for the router not to reboot. It's important to remember that very few routers are affected.