Amps can use peak current greatly in excess of the nominal usage. A power conditioner, no matter how well made, incurs some loss in the capacity from the outlet it feeds from. The more amps you connect to the power conditioner and or the closer you run the power conditioner to its rated max, the bigger the problem with limiting peak current.
Aside from this explanation is the one from a number of people in the know. Many amp manufacturers state that power conditioners are not a good idea for their amps. I have talked to the makers of a few conditioners I respect and they state it is best to leave the amps off. Based on their experiences and feedback from customers.
Finally, the technique I always use on questions such as these is try it yourself. The best answer is your own answer.