UTV battery not holding charge

I have a 2008 Arctic Cat Prowler that has maybe 150 miles/30-40 hours on it. Anyways, I bought it slightly used and when I did the gentleman said that he had just replaced the battery because the other one wouldn't hold a charge. Well, the new battery doesn't seem to be able to hold a charge either. I charge it up all the way, then if it sits for 3 or 4 weeks, it's pretty much dead. What would cause the battery to drain? The key is always off when not in use. Thanks for any help.

Not sure, but if the battery is indeed good the only solution I can think of is to get a positive terminal switch so you can cut the power off all the way. Or maybe you can get a solar panel to put on it? Just can't think what would be pulling juice!

#1. Have the battery test and make sure its good and not deteriorating or self dischargeing.

#2. Determine parasite loads by disconnecting components or isolating. Total parasite loads should be less than 10 to 30 Milliamp at most.

If it has a Alternator?, it may have bad isolation diodes.
If MotoGen it may have field windings that are breaking down and draining bat.

Other parasites: Electric hourmeter, clock, radio memory, electric engine/fuel management?

Remove the battery charge it fully then get it load tested.
If it fails replace the batt, if it passes clean the terminals on the battery with some very fine sand paper or a small bronze brush.

Pass or fail you should next clean the cable connections and follow the negative cable to where it's grounded remove that connection lightly sand or brush it clean then tighten it up.
The regulator / rectifier should be under the drivers seat next to the battery remove and clean those connections inspect regulator for dirt / water intrusion, reinstall battery tighten everything up.

Start the engine let it warm up, using a multi meter set on DC voltage the no load volt reading from the batt at idle should be 13.2v +, with lights on 12.6v+.
With lights on slowly rev the engine watching the multi meter it should increase with rpm to a WOT max of 14 ~ 15.5v.
With a known good battery and all connections clean and tight if the voltage rises above 15.5 the regulator/rectifier is faulty.
If the voltage fails to rise at all or doesn't rise to at least 14v the stator/charging coil needs to be tested.

A bad regulator or short the the stator will drain the battery.

Thanks for the info. I'll follow these steps and see what I come up with.

atv batteries are short lived mine went bad in 2, i keep a tricle charger on mine when not being used