You don't know people here, or Seth, however, even as an absolute stranger, Seth's comments deserve at least some testing. Do you have any other speakers (or a friend, etc) try them with your amp and see if it cuts out like it does now. That will determine if the speakers are the source of your amp's problems.
Of course, we have no way to know the problem is the speakers, it may well be the amp or wiring, but you should investigate before buying an amp.
Also, do a close visual inspection of your wires as well as the terminals to make sure no stray wires are touching. My brother's cat had dug his claws into the speaker cables and it behaved just as yours is - works at low volume, but when you crank it, it cuts off. He only found out after replacing the amp that the first one was cutting out via the protection circuit.
Unfortunately he had worn out the protection circuit by the time he figured it out. The first amp worked better, but never would run full volume after the cables were replaced. The second amp is still running fine.
However, either way, you do have white van speakers. If you decide to keep them, hopefully they will not harm your other gear.
I think it is not so hard to determine the true worth of these speakers. Just weigh one of your towers. Then find a tower of similar dimension with similar drivers that you think of equivalent quality and see what the published weight is. A good speaker has heavy magnets for the drivers and a solid, braced cabinet to control resonance. You can't really cheat on weight (you probably can a little, but weight is typically not a concern for speakers, so why spend the extra money).
If you are here in the states, go to Best Buy and buy a pair of Pioneer BS-22 or FS-52 speakers (about $140/pr or $280/pr, respectively). BB has a 14 day return policy (be sure to keep all packaging, manuals, etc). Test your amp with them, and compare the sound quality.