Hello Rhharris,
Most speakers require only a few watts to play at a moddest level. However, anything with a dynamic passage whether it be a horns, cymbals or drums can require as moch as ten fold. Essentially, what happens when you play something requiring a great deal of power the amp provides what it is normally capable ofand, since the sine wave cannot be completed it simply squares off. Think of an ice cream cone with the top cut off. Hence the term "clipping".
The other expressed conscern is the fact that your speakers present a 4 ohm load. Taking this into consideration it is unlikley that clipping is the case. Think of ohms, in which is a measurement of resistance, as a group of people guarding a doorway and current as an other group of people trying to pass through that doorway. Simply put, the more Ohms (guards) the less current (people) will be able to slip through and vica versa. Because your speakers offer a lesser load (resistance) than your amp was presented with when its output was measered, it can actually produce more than 60 watts without "clipping". Thus, I would conclude, as Sean suggested, that you are driving the speakers too hard not the amp.
I would also agree with Elevick's suggestion. Limmiting the bass responce to the speakers no only takes the strain off your amp but more importantly your speakers.
Happy Listening
Damon