There are two items to look at when diagnosing this problem:
1. If you have updated your relays, then you need to make sure that you have replaced the two circut breakers that are included with the kit with the current flowing in the same direction as the older breakers have. The wires from each side of these breakers is not interchangable. If you have mixed up the wire connections, then the breakers become overheated and will cycle the cooling fans because they are overheated. A good clue that you have this problem is to check and make sure your fans cycle as they should when your engine temperature is calling for the fans to cycle on and cool the radiator. If you are not having a problem overheating when you run the air than this probably is not your problem.
2. There is a low pressure switch located on the passenger side of the car, mounted on the dryer assembly of the air conditioning. If you turn your front wheels all the way to the left you will be able to access this switch without jacking the car up. Behind the left front wheel is the dryer/switch assembly. There is a three prong plug that is attached to this switch. Pull it off and underneath is a fitting that can be moved with a pair of needle nose pliers either clockwise or counterclockwise. This switch controls the cycling of the air conditioning compressor based on the low side pressure of the air conditioning. Start rotating the switch in slight increments until your cycling starts to extend to what is recommended in the Delorean manual. My manual indicates that the cycling time should be between 45 and 90 seconds. This time will be dependant on ambiant outside temperature and humidity at the time you are trying to adjust this switch. If by adjusting this switch you cannot adjust the cycling time you should consider replacing this switch. It is very inexpensive, 12 to 24 dollars and since this is a Harrison system, many GM autos of the Delorean vintage use the same switch.
If you have any further questions feel free to call me at 708-672-5439 direct or fax me at 708-672-5408.