I've had a similar problem like this in the past. The problem seems to be that some active device in your audio chain, most likely your amp or Head Unit (if you're using one), is going into thermal/electrical protection mode.
The first thing I would check is whether your amp is overheating, the the HU. In my case, the problem was a defective head unit that went into protection mode for nothing, and I have a seen a Kenwood sub amp overheat in minuted because of a defect and also shut down.
So it's rather unfortunate for you, but I'd say chances are either your amp or HU will need to be repaired or replaced.