9yr old model Maytag window a/c - just blows cold for 30 seconds - then blows warm. Was perfect until this happened. Is it worth fixing? What would be the usual fix for this?

Probably!

Have a pressure test done on your cooling system, you sound like you could have a leak in your system or your system just needs to have the air bled from it. Check your coolant level also, with air in the system and not enough coolant it will blow cold and cause overheating.

Proper make & model of furnace please.

Sounds like one or more of ofvyour 3 defrost components have failed which are defrost heater , defrost thermostat, and defrost timer or board

are they putting in the right ptc overload relay? there are 2 styles for this model,remove the old one off the compressor body in the lower area of the unit and take it and the full model number to an appliance parts supply warehouse and they can check and make sure you had the correct one before,and can get you the right replacement if the old one is bad or incorrect

Should be worth fixing. Belt kits for Maytag A511 washers are still available on line (about $30).

"it seems to work fine but will not get cold"
Not sure how it can work fine and is not cold. When you say work fine, is the light on and the freezer fan blowing but is the compressor running?

Unplug the Ref and wait about 30 min or so, plug it back in and listen for the compressor to start running. You should be behind the Ref to hear this. If you don't hear it start running then you may hear a clicking noise. This clicking is a problen with the compressor start relay. If the compressor runs but still is not cold then it could be low on coolant.

being a maytag about 30 years old i would say the belt is broke or transmission is locked up ,,,, if it was a newer style you may have difference problem that could be easier repaired

Defrost system problem related to defrost timer or heater circuit. Possible open defrost termination thermostat or open defrost heater. If timer is bad it will not go unto defrost automatically but can be manually started from the timer by rotating the clutch head screw slowly clockwise until you hear one click. If the system fails to restart after 30 minutes rotate slowly again until you hear another click and it should restart. If you had to rotate the timer the second time the problem is a bad defrost timer.

Not sure which model you have but i would check your indoor and outdoor temperature sensors  and also it could be your overload kickin the compressor off