I am using a monoprice speaker selector with a powerful amp (300 watts a channel, 2 ch amp). In running this combo in which selector is only rated for approx 80 watts max, can it cause fuse to blow in my power amp? The set up runs for approx 10 min before blowing fuse, and tends to do so when I increase volume.
You havent stated how hard you are driving the amplifier before it blows a fuse. Frankly, more than likely the fuse blown wasnt related to the wattage but most often an impedance issue. Check your wiring.
If your speaker selector has impedance matching, so that the amp doesn't see a load it won't like, then you could damage the selector with an amp that much larger than the selector can handle.
If it doesn't then your amp may be seeing less of a load than it can handle and that blows the fuse. DO NOT PUT A LARGER VALUE FUSE!
Get a speaker selector with the right power rating and impedance matching. Not cheap if you have a real 300w x 2 into 8 ohm amp. I suspect that you don't. Many cheap amps have bogus power ratings and won't handle much in the way of real life speaker loads.