99 Suburban AC Problems

I own a 99 Suburban with 71,000 miles and dual AC.  I use it mainly for travelling and short rips to town occasionally and have developed a strange problem with the AC.  It runs fine and will freeze you out when you first put it on the road.  However, if I stop & shut down for a few minutes the AC will not kick in again until you get it on the road and run it for several miles, then it runs fine again.  If it sits for longer periods, say a couple of hours, it comes up fine again.  I have even tried leaving it running while parked and it will shut off after a few minutes at idle.  It did this only once or twice over the last three years but now it does it almost every time I take it out.  I first suspected somthing electrical & heat related because it only does it on the hottest days.  I have changed out all the relays I can find and no change.  I recently took it to the dealer who said it was low on freon and I had a leaking compressor.  The solution - a new compressor for $1000 minimum.  I asked why it would work after a few miles at highway speed and he said it took the compressor a while to build up pressure again.    I was also told that I should not expect to get but 4-5 years out of a compressor.  What a deal...by the mileage you can tell I haven't gotten that much out of the compressor!  The solution sounds a little too cut and dried to me.  I have also started to experience a few other electrical related problems within the last month.  Any connection?