In the case of an external power cut, ie failure of the whole street supply, I can imagine reasons why DSL could perform differently afterwards. In the process of restoring power, some engineer from the supplier will have fixed a fault and in doing so, may have disturbed, or altered, something else. For example last time we had a power cut, after it was ‘restored’ I checked the voltage and it was way below legal minimum. I then had to reported that as a new fault, which was duly rectified.
But if the whole house trips in a fairly modern house, it is probably an RCD that has activated. These devices detect any imbalance between live and neutral, so they will trip if an appliance has leakage to earth. Their starring role is to trip if a human touches a live wire, hopefully cutting the supply before death occurs, so they are impressively sensitive and pretty much instantaneous. Tripping current is usually 30mA, about 1/1000th of the current it might take to blow a main circuit fuse or MCB. No big flash and bang, just a gentle ‘clunk’ as the power is removed.
But as far as the router is concerned, as far as I can see, a tripping RCD would be no different from simply switching it off at the mains socket. And resetting the RCD is just like switching it on again, hence I can’t see any reason for lasting effects. It may be worth wandering around the house with an AM radio, listening for noises... especially perhaps, near the oven?
