2004 Volvo S40 Air blows cold then quits

I dont know if you have the new style S-40 or the old style before Ford took. Also your qustion kinda confused me? The A/C works and then it blows cold air? Do you mean it blows cold air on it's own? I am going to assume it does not. The problem you may be having could be the A/C compressor clutch failing. Quick way to test this is when the A/C compressor quits while it is still running and not touching any of the A/C controls have your mechanic check for power at the electrical connector to the clutch. If you do have power you know the clutch is bad. If you do not have power then further diagnosing is required. Also measure the gap on the compressor clutch. Specs call for 0.3mm to 0.5mm when you remove the belly pan you are going to see a lot of brown dust from the compressor clutch wasting away.