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well, I guess this depends on two things:
a) are they under warranty
-and-
b) do you have any electronics experience?
if no and yes...
then you need to disassemble the amplifier section of the speaker and check:
a) that the final amplifier transistors are properly mounted to the heatsink and have heat transfer compound between them and the sink
b) that no single component on the board (not just the transistors mounted to the heatsink) is running too hot (check EVERY component on the board just after it shuts down)
c) check for voltage from the power supply just after shutdown -- if the power supply is not providing voltage anymore the protection circuit kicked in, or the power supply is overheating or otherwise dying.
regardless, it sounds like a heating issue... or something otherwise tripping the protection circuitry. there may be known problems with these puppies, but im not familiar with the crest internal amps... you might give crest a call and talk to a tech, see if they can advise you on common malfunctions on these models.
for shits n grins, is there a vent, or a fan? maybe the fan has stopped spinning or a vent is clogged up with dust/debris/other junk ?
this is why i cant stand powered speakers. it doesnt take long before the amps act up and then the whole cabinet is just useless. so much nicer to just switch to a backup amp and troubleshoot the standalone amp at your leisure! 9 out of 10 times the failure is the amp, not the a passive crossover or driver unless you really rag on your speakers and dont have a limiter 
good luck 
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