subwoofer motorboats between songs

I built the parts-express 8" sealed sub in their .75 cf box. Being small and sealed it takes a quite a bit of power, but it is for a small system in a small room and it does sound good with a 100 watt amp for that situation.

The problem I'm running into is when I stream music through jazzradio.com; during the quiet parts, between the songs, the driver flops around making a motorboating sound. It doesn't do it when I pause the playback or between songs on other sources.

Both of the subwoofer amps I have top out at 100 watts, one is a class D OSD amp and the other is an A/B dayton plate amp. To get the right level of bass they have to be turned up quite a bit but sound perfect during the music.

Obviously, there is something in the source that is causing the problem but my 2 store bought subwoofers, that don't need the volume cranked as high, don't make any noticeable sound between the songs, when swapped into this system.

The question is: Do you think this an issue that is only being made audible by pushing the 100 watt amps to the edge of their capabilities? I hate to buy a 250-300 watt amp and have the same issue.