If you made sure that all connections of the cables both at the plug you stick into the Pi's jack and at the socket / jack at the other end of the cable (where the earphone is plugged in) are properly isolated, there should be no issues in leaving the cable in place all the time.
Note that the sleeve of the jack is connected to the video signal (see here). If the cable allows the jack to move around, its metal might short circuit to other parts of the Pi, i.e. the GPIO header or other connectors. Make sure to avoid that.
Mechanically I would not expect any wear and tear due to a plug being permanently plugged into the Pi's A/V jack. If anything connectors are worn down by mating cycles, i.e. the plug being repeatedly plugged to and unplugged from the receptacle. Expect the number of mating cycles to be in the range of a few thousands though (for a jack of reasonable quality).