I had a similar problem, had to mess with the compressor clutch it was worn off to the point where it would not engage after the compressor gets hot and the gap is too far.
Could be a lot of things as I have come to learn. But I would start with the cluth, if that's the problem a simple fix would be to take it off and remove a spacing washer that is put in to space it in the correct distance away from the fly wheel of the compressor. If the distance is too far the magnetic coil can't attract the clutch and get it to work at all.
A simple way to find that out is to look at the compressor and if the fly wheel is not engaged when your ac stops working that most likely is the problem.
But considering the fact that it does work and then stops means that the relays are most likely ok. | 
