Many/Most home-level NAT routers can't support passing-though multiple, simultaneous VPN connections at once.
They get confused on how to rout the traffic, and the only way to fix it is to clear the entries from the router's routing tables. This will happen after some amount of time (after the VPN is disconnected), or you can usually force it with a power-cycle (like you're doing).
Depending on your router, you may be able to upgrade it to a 3rd party firmware that will support it.
Otherwise, the long-term answer is probably that you'll have to go buy a more robust router that can handle the multiple, simultaneous VPN pass-throughs.