Subs going off and on

The problem you are describing could be caused by numerous problems.
I think you might be on the right track by starting to look at power issues.
First be sure that your battery terminals are clean and connected to your battery tightly. Make sure that you have a good battery by having it checked out by your local autoparts store who will usually check it for free.
The amp needs to have the proper size wire between the battery and the amp, fused at the battery and the amp according the mfg specifications.
Just as important as the positive battery wire from the amp, be sure that the ground from the amp is secured to a solid paint free metal that is commonly grounded to the negative side of the battery. I am assuming that you do not have and old vw, positivly grounded car or some other weird car.
If the power checks out with the battery, make sure that your car's charging system is up to par. If your stereo is requiring a lot of power, you may need to upgrade your cars charging system.
Another cause of the amp going on and off would be the use of too many speakers or blown speakers. You need to check the mfg specifications for the amp to ensure that you are not overloading it.