Dodge Neon Sputters with A/C on

After a while of running with the A/C on the car starts to have little hiccups? almost sounds like it’s missing? but not that dramatic, it will continue after I turn the A/C off, but resolve after I have had the car off for a while. It will start up again after an hr or less of starting the A/C. It seems like I have a loose in HP while this is happening, more so than normally expected with the A/C on. I have recently replaced the ignition cables, plugs, my car is definately a little more peppy now, and had the timing belt/water pump replaced, all the ussual maint, but this issue was present before. Any ideas what this could be? Thanks!

Are you sure that if you drive without the AC all day, the problem never occurs?

Check battery voltage with the engine idling.
Does it drop significantly when the AC is turned on?
At any rate it shouldn’t drop below 13V.
How old is the serpentine belt?
It could be slipping under the extra load of the compressor, causing the alternator to slow down.

@Insightful: Yes, it’s only when the A/C is on.
@Circutsmith: I will have that checked.