I don't have a stabilizer at hand, unfortunately - I don't know anything about this apart from what I've learned from google, but you're saying that a stabilizer would make up for the fact the power adapter I'm using is unregulated?
So, having an unregulated adapter as opposed to an adapter with a voltage regulator could cause a problem like this..? If so, could buying a regulated adapter @ 12VDC 3A solve the problem? *Also (this question proves how little I know), would it be ok/wise/safe to use an adapter with a slightly higher amperage than 3A, say, 4.8A?