The power supply for the speakers is 120v input & 7.5v ac output.
this might be the problem, the type of power supply
you have a double conversion going on
120v to 7.5vac
then 7.5vac to DC inside the speakers
when the speakers and TV are off..you still have voltage and conversion in the first power supply
IF it were me
my next set of speakers would be, the type where the 120v goes directly to one of the speakers, the DC conversion has less steps involved
i have a set of speakers just like that, i occasionally use with my laptop
they might last longer in your stituation
and yes i run all my entertainment from an inverter
i don't think the problem is your inverter
i think its the design of the speaker system