not unless the invisible fence operates on 315 MHz frequency
"Everything causes [radio frequency] interference, believe it or not. Everything."
Consider the so-called internet of things: Wi-Fi-enabled refrigerators, slow cookers, coffee makers, fitness trackers, pet fitness trackers, sex toys, and — for some reason — flip flops.
BUT they don't operate at 315 MHz
One other thing that should be checked, is the vehicles battery, if it is as low as 11 volts, it could cause the FOB to malfunction.
Again, this does not seem to be your issue, if it only happens on your property.
Has your Power Company installed a new Power Meter ?
some of them have a transmitter built in, so no one has to go to your property to read your meter