Assuming you have eliminated the amplifier and source, the most likely reason the speakers cut out is that the midrange and/or tweeter are blown. In this case the voice coil may be rubbing against the housing and they only get over the resistance or friction at higher volumes.
B&W 802 Nautilus speakers
When playing music with the B&W speakers they will cut out with no sound and then the sound will return. at low levels this happens but not with higher volumes and the sound and does not cut out. The amps that I'm using are brand-new so I want to know if you think the crossovers in the speakers are bad?