Sigh; " I called for a service technician to look at it and he said he's not sure why it is short cycling, but said a new compressor is the fix. " = CALL SOMEONE THAT KNOWS WHAT THEY ARE DOING!
sorry.. sometimes I have to yell.
Anyway; It's fairly new. No one should assume first, that it needs refrigerant. Short cycling could very well be power supply related. These little 12/24 volt compressors have a very, very sensitive volt, amp, resistance controller. (costs as much as a compressor even)
All power, connections, wire size, and battery power need to checked and scrutinized. 3-5 amps continuous is about the needs of such units.
Now, if it's still short cycling, it could just be the location of the the box thermostat or it's sensor. When it's running; you should hear normal gurgling sound in the plate or evaporator. If the whole plate gets cold and iced after running It's most likely ok with refrigerant.
You need to ask questions of techs you are thinking of giving the privilege of servicing your unit. "Are you familiar with 12/24 volt power supplied units?" Do you know how to handle refrigerant evac and replacement in very small units?" (only one answer; "weigh it in ounces" Do you know check out procedures of Danfoss controllers on 12 volt systems?"
IF,, and I stress IF.. it does need refrigerant (newer, most likely is. 134-A) "Top it off" is a dumass procedure based on hope rather then knowledge (yes we all do it,
) Most systems I've been seeing and reading about, only hold a few ounces. NOT pounds! like domestic refrigerators, when was the last time that needed gas?
Hope this helps!