I have exactly the same problem on my 2000 V70 (100500miles) which I have proved to the compressor clutch. After considerable wear the air gap increases and as the engine compartment heats up, the clutch fails to pull in. To prove it, try the following VERY CAREFULLY! The compressor is below the alterator and driven by the same auxiliary belt. While the air con is working, you will see that the clutch on the end of the compressor is rotating. When your fault develops and you see that the clutch is not rotating, with a long piece of thin wood, very carefully give it a gentle tap, taking care to keep away from the auxiliary belt. If the clutch kicks in, that is probably your problem.
I have not yet sorted mine out, but today got a quote of £150 ($280) which if you go to a dealer will probably be $600+. My ex-Volvo mechanic friend says it is a pig of a job! However, a respondent to my question on the UK Volvo Owners Club web site has advised how to do the job without disconnecting the pipes. Ignore the first reference to a SAAB compressor, but have a look at the penultimate one from Chris Rogers:

http://www.volvoclub.org.uk/dc/dcboard.php?az=show_topic&forum=14&topic_id=12882&mesg_id=12882&page=1

Let me know how you get on.

Graham