As for your choice of woofers, I would only go with 600 watts or higher if you get a new amp--because you know that maybe you don't ABSOULTELY need it now, but you will later. Also, the sound can seem much clearer and you will love it when you hear the bass =)
Weellll... I would argue this a bit. The amp I mentioned before I think is a 1000 Watt tube & analog based amp. Personally, I dig the resonance and full-sound of the older style amps.... as many "old-timers" tend to... funny enough, I'm not much more than 22 years old.. haha!
back to the cutting out, I would agree with last-wish that it could be an amp difficulty.
My same friend with the 1000 watt amp from the 80's had purchased an amp from a pawn shop which when hooked up to more than 2 speakers and when cranked past 1/4 volume, would cut out the lower end bass hits.
Now that I have given it more thought I would say it is your amp that may need changing. If it's 200W per channel, then it should be fine, but, if your volume it up a little too much with more than 2 speakers and it's cutting on the bass... I would say "new amp time"
Look at some old pawn shops and salvation army type stores. I think that's where my friend got that 1000W amp that litterally makes your ears bleed at 1/4 volume. :-)
This also brings to mind the time when we had a 400W Subwoofer attached to a Sub Woofer Car Amp that was at 200W per channel. Well, it managed to cut out at any bass hit at all, period, which had anything below the low mid range. We decided it was underpowered, and got a new amp for the pair of subs :-) which fixed the problem.
Before you run out and get a new amp though, test out your speaker setup with someone elses amp of more power with your system and see if it cuts out. Just borrow their amp for a few hours of something. If they are powered fine, then you know it's the amp. If they cut out, then it's the speakers... but I am going with last wish on this and saying it's the amp.
Peace!