Could be the compressor locking up on a restart. Mine was doing the same kind of thing. Then a buddy of mine who does HVAC for a living said the compressors are very reliable and it's almost always a case of bad capacitors when your AC won't kick on.
I opened up my 32 year old rooftop Coleman AC and discovered the capacitors were all leaking. I replaced them and it now works GREAT!
Be very careful when dealing with capacitors. They hold a brutal charge and really can hurt or kill you. If you are unsure about it, see if you can contact a local HVAC guy to come open it up and help you order/replace them.
Jose