I checked the compressor clutch as suggested by some. It's engaging and rotating with the compressor fine both when the cooling is good and when it stops.
I guess a technician will be able to diagnose the problem best but I'd really appreciate someone interested in fixing my current system rather than asking me to get a new AC unit installed for maximum profits.
I'd like to mention a problem which I'm not sure is relevant to this problem: the blower speed is really low. Even with fan set to max (4th position), the blower's throw is is really low (about what you'd get at position 2 in a properly functioning system). I asked my local technician to try replacing the blower. He used a Cultus blower and the throw IS EXACTLY THE SAME AS BEFORE. Not even 1% difference.
If changing the blower didn't increase the air throw, what could be the problem? And could this be related to the problem of AC cooling dropping off after running for a while?