I would guess, that you have either an exp valve going bad, or a blockage developing in the rec/drier. Fans of course can cause this, as has been suggested, but if your on/off minutes count is correct, I think your problem is with freon flow. If you have a lazy exp valve, with the orifice pin not rising high enough, the a/c will get very cold, just before the system shuts off due to excessive evap temp. A bad evap temp sensor can also cause this, but this is fairly uncommon.(you can check this in the self diagnostic mode) A sticking exp valve will also cause excessively low pressures which can also stop a/c.
A rec/drier that is blocked, or has enough moisture in it to freeze (another form of blockage) will cause liquid side pressures to rise rapidly, also killing the compressor. This condition also takes more than a minute (usually) to 'normalize'.
All this, without gauge readings, is just previous experience. Check the fuses suggested, and do the self diagnostics- beyond this, the next step will be gauge readings, IMO.
HTH,
MB