The a/c typically cycles for a couple of reasons, the most common is low refrigerant levels. It will also cycle if you have it set on a low fan speed to keep the evap from icing over. The reason it cycles when you are low on gas is that the low side pressures get to low and the cycling switch opens. At idle the compressor is not spinning fast enough to get the pressures low enough with the quantity of gas you have in the system. When you come off idle and the compressor spins faster the low side pressure drops, the cycling switch opens, and the compressor clutch disengages. Now if you had the correct amount of gas in the system it would not be able to get the pressures low enough to cause it to cycle. So with it on high fan speed, rev it up and see if it cycles, if it does you are a little low on refrigerant and need to either top up the system or do a complete evacuate and recharge of the system. You can try tightening the schraeder valve in the low side fill port or just replace the darn thing. I own a shop and have to guarantee my work so I do not dick around with tightening stuff, I stuff a new one in it an be done with the damn thing. Seeing as how you obviously have a leak, it would be nice if you could put some UV tracer dye in the system while you are servicing it.

Mark