Just to confirm here, how do you know it's "cutting out"?
1) When plugged in to the AC, does the green LED on the charger go out, and/or does your menu bar icon indicate that you are running on battery power (i.e. a black bar in the icon, not a plug or lightening bolt symbol)?
or
2) Does it charge to 100% and then just slowly drain (based on % reported in the menu bar) with the green light on the adapter plug glowing the whole time?
If #1, an
SMC Reset may correct the problem. Two of the symptoms listed on the linked page are: "not charging the battery, or not recognizing the AC Adapter." It could also be a faulty adapter, or something as simple as debris in the power port preventing proper engagement of the pins.
If #2, there is no problem. That's normal behavior, and if you click on the battery icon to view Time it will report "charged". Your MBP will not initiate charging if the current charge is 95% or higher (to prevent overcharging the battery), and the MBP will occasionally draw power from the battery even while on AC, because occasionally the processor demand for power will momentarily exceed what the AC can provide (this is the reason that if you run on AC without the battery installed - which is
not recommended - your MBP throttles back your CPUs to 1 GHz).
Hope this helps...if not, post back.