If your amp is cutting out its not because it needs help..
http://www.cardomain.com/sku/JVCCSWG1200
If these are the subs you have..do you have them wired to 2 ohm? series/parallel? If this is so then you probably are giving them pretty good power from that Kenwood amp..may not be meeting the subs rms tho. IMO I'd sell the Kenwood amp and buy a JBL 1200.1 (apprx. $280) and send 600w to each sub..they say that the peak is 1000w on your sub so I think they'd handle it pretty well and sound ALOT better.
btw..how do they sound now?