I have a 2000 SE with the same problem. The dealer and my independent can't find the problem. In my case, it seems as though the compressor is freezing up. I shut the AC off for 10 to 15 minutes, let it "defrost" and turn the AC on again. This will typically allow my unit to cool for about 45 to 60 minutes prior to occuring again.

When this occurs on my car, the fan gets a low, gutteral noise, and stops blowing as hard as it should be.

Everyone is stumped and I think I'll just have to live with it at this point.

When you say the fan fails does it stop blowing air?
Or, is the air that comes out not cool (but it still is blowing)?

Fan failure is common and the fan is easily replaced.

AC blowing warm air after a period of time is also a common
problem. Typically the AC compressor overheats and shuts
down. Low refrigerant can cause this. Also, Volvos have an
overheat sensor on the compressor and some of them seem to
be a bit too sensitive.

On a 100 degree day my 98 S70 will only blow cold air about
15 minutes. Then blows hot air for 10 then back to cold
for 15. It is low on refrigerant and I plan to have it
re-charged for next summer.

A good dealer with good techs would be well aware of these
common problems.