I've seen this problem with some AC units.
There are a few pressure switches ... usually one on each side of the compressor.
One's a High and the other's a Low Pressure switch.
With the system off, the pressure on both sides of the compressor will "even out" - since it's a closed-loop system, the pressure will equalize the longer the system is idle or not pumping.
But, when the pump starts, there's usually a "delay" switch that will prevent the compressor from shutting off for a preset time until the system has a chance to build up the right pressures on both sides of the compressor...lower pressure on the supply-side to the compressor and high-pressure on the exit side of the compressor.
If the "delay shut-off" relay drops out and either one of the the pressure switches is in an "off" state or "THERE'S SOMETHING WRONG HERE!" state, then the compressor shuts off for a predetermined time, then it will either try again or in a more expensive situation, trip out and then send an alarm to a monitoring point or station.
Since it's been 6 years since you've had it installed, the question, first, would be: When was the last, if ever, time you had the unit serviced? If never, now's the time to call in the calvary.
The best time for doing any of this work is usually during the begining of the cooling season for ACs...the service techs like to see the ambient air temperature around 75° to 80° and a relative humidity level of something just about the top end of "comfortable" - whatever that is...
As for a HP? That's their call. They probably have a "balance point" for ambient air and humidity that's an all-around good testing/setting-up point that works both sides of the seasonal setup for their gear.
GL and let us know what happens!
BTW: I've seen AC Techs use a standard tire guage just to check to see if the system has ANY gas in it. CAUTION; NEVER WHILE THE SYSTEM WAS ON/RUNNING. ONLY WHEN IT WAS OFF AND THE SYSTEM HAD A CHANCE TO "BALANCE OUT" - through years of experience, some of the techs were able to tell if a particular system had enough "juice" or not by just what the stick told them...and usually, after cleaning the fins and compressor out, they'd be within 40-60psi on the high-side and about 0-5psi on the low-side. Experience shows!!!