I understand how you feel. I felt the same before I understood how the BMW AC system worked. I talked to a lot of techs and waded through a lot of vague info on-line to get a basic understanding of the system.

The E53 X5 AC system uses a variable displacement compressor. That means it does not depend on the compressor magnetic clutch engaging and disengaging a fixed stroke compressor to control refrigerant temps...a mechanical control valve inside the compressor senses pressure differential of inlet and outlet pressure within the compressor and alters the compressor stroke itself for optimal compression.

This kind of system has the compressor clutch engaged all the time as long as the AC is on and there is refrigerant in the system. This threw me off at first as I always assumed an engaged magnetic clutch means a working compressor. In these variable displacement compressors, this is not always true.

Do you have access to gauges? Hook them up and you will notice when the AC is cold, the low side pressure will be in the 30-40 range. When the AC stops cooling you will notice the low side pressure rising. And all that time you will notice that the magnetic clutch remains engaged.

In a standard fixed stroke compressor, no cooling plus elevated low side pressures indicate a worn out compressor. It no longer compresses the refrigerant. It indicates low/loose compression.

In this case it cant be a worn out compressor as there is good compression as evidenced by the cooling and verified by gauge readings. It just happens to be intermitent.

In variable displacement systems intermitent compression usually means the control valve is not working as it should. There is no compression when there should be compression.

The fan is not working because the pressure switch that turns it on does not see any pressure in the system, because the compressor is not compressing...the fan operation is a symptom and not a cause.

When the compressor starts compressing, pressure rises in the system and the fan then operates normally.

I hope that made sense.