My amps have always had it, but my mates little Sony amp doesn't have any LED's at all! I'm pretty sure any modern amp has a protect mode, but it seems that they don't all indicate when it is in effect.
When his cutout happens, it can stay off for quite a while.
I told him that his power could be shorting on the body... he has a large power cable from the battery to the boot, with an inline fuse. I mentioned that the voice-coils could be shorting on the speakers, but when we lifted the parcel tray manually, nothing happened.
I was going to loan him my amp to see if the problem persisted, but I don't think he wanted to go through that much effort.
I'm still leaning towards a speaker malfunction, which forces the amp to shut down. (protect mode).