question about the base going in and out on 2 10 inch kickers.?

Hi .

I have the following set up on a 08 honda civic LX

Stock radio.

4 alpine speakers (stock placements)

2 alpine tweeters (on the tweeter slot by the windshield)

2 10 inch kickers in a ported box .

Alpine 500 watt amplifier .

I pride myself on being able to keep a stock look because the car is parked all day at a train station and it is important not to attract any attention to it.

the problem is that when the music is playing , the bass will cut in and out regardless of the kind of bass or song , it can be Madonna hard candy or Andrea Bocelli for that Mather and independently of volume ,

When the base is going it sounds nice and clean for the most part , I have also inspected the amp to see if the blue light on it cuts off when the bass cuts but it stays on and no visual or audible evidence to point out to be a cut of power .(you know like when the power comes back and the speakers jump or you hear a pop)

The amp is connected trough an adapter connected trough the rear speaker since the stock radio does not come with an RCA jack.

The problem started when I went from 1 10 inch kicker to two 10 inch kickers , before it was fine .

What could this be ?

Thank you .