1995 Mustang A/C compressor Cuts in and out

Hi all. I'm new to the Mustang world. I'm a V-Dubber, but my wife bought a 95 'Stang the other day. We got the car for $2100 so I figured there was some stuff wrong w/ it. The door hinges on the driver's side need replaced and some other small stuff. I forgot to check the A/C at the time, but got home and it doesn't work. I started checking it out. The compressor was unplugged. Cleaned the corrosion off hooked it up to 12v and got the compressor going. Hooked it back up to the system. Checked the low pressor switch and cleaned it up. Now it works, kind of. It runs for a second or too and then shuts off for about five seconds. I know there is a leak in the system because i have charged it a few times and it has gone back down. So I ran the ac full blast while charging it and it does the same thing.

My question is basically is the compressor bad, or does it keep kicking off because of the lean and my little can can't supply enough volume or R134a to keep it going and the pressure switch keeps shutting it off.