I assume that when you mentioned that the recharge only lasted for a month, that was until the a/c stopped working again? Usually a/c stops working when there is not enough pressure in the system due to it being low on refrigerant and given how long a non-leaking system normally lasts without a recharge, you've got a fairly substantial leak in a/c terms.
You can probably get away with a couple more recharges but keep in mind that the refrigerant also includes the lubricating oil for the system and if you keep topping up the refrigerant, the ratio might be off, which can do further damage to the a/c system and your wallet.
I would consult the local yellow pages for an automotive a/c guy - a lot of garages (especially the smaller ones) don't have the gear and licenses to deal with a/c anyway so they often farm it out to a mobile guy. Getting said mobile person to come out and check out your car's a/c will at least save you the overhead the garage charges on top of what the a/c person charges.
Also, the reason that they're only quoting you for the diagnostics is that in order to find a leak, some refrigerant will have to be replaced by a UV dye, then you get to run your car for a few days with the a/c on before the actual leak check can be done. Only at this point it's even possible to figure out what needs replacing as it can be anything from the compressor to a line to the evaporator or receiver/dryer. And without knowing where it leaks you can't diagnose the problem in the first place.