It sounds as if the DC offset protection is operating on that channel, probably from a failing power transistor.
To make sure the problem is in the power amp, see of the left channel cuts out on headphones. If not, you know it is the power amp, and the preamp is OK.
If you don't want to ditch the receiver, buy a two channel power amp for the left and right speakers and run it from the preouts. That will almost certainly be cheaper than the cost of repair. That will also be an upgrade.