Does the AC light come on when you try to operate the AC and do you hear a click when you turn on and off the AC switch. You should hear a click from the air conditioning compressor clutch when the AC is engaged and released. If the system has a leak, refrigerant will be lost and the cooling efficiency of the air conditioning system will decrease. The system may need a recharge and or the source of the leak investigated and repaired.
Honda is aware that the the crv 2002 has an aircondition problem and will replace the ENTIRE SYSTEM if you press the issue. This is also a problem on other models including the pilot. THe system gets contaminated and just replacing the parts i.e. compressor,air drier will not do it. The entire system must be replaced and honda does not like to do it. They split the bill ($3400) with me, I paid $1400 they the rest. Car had 87000mi. This should be a recall for sure.