I'm losing automatic transmission fluid. Is there any common history to support a theory of leaking transmission cooling lines?

Why Is My Automatic Transmission Slipping? If you have an automatic transmission and it "slips" while you are driving it-that is, the car engine revs without the power going to the wheels-the most common cause (though not the only possible cause) is low transmission fluid. If the slipping is caused by low fluid, it will get worse as the transmission gets hotter.
Why Is My Manual Transmission Slipping? A standard ("manual") transmission uses fluid too, but leaks aren't a common issue; a standard transmission could lose all its fluid and never slip at all, though eventually it would lock up while driving down the road. If you have a standard transmission, and it's slipping-the engine revs but it doesn't transmit power to the wheels-the problem is usually in the clutch.
Further down in the article I discuss how to diagnose this problem.
Sounds Like Low Transmission Fluid to Me

How much "over full"?
(Realize that the fluid level will be slightly higher when the trans and fluid is hot, and lower after when the vehicle has not been running and cold).
If it is only 1/4" (~10mm) overfull, that could account for just normal fluid temperature expansion. Anything greater than that may indicate the following problem.

That said, if the fluid level is significantly higher than normal, there is only one place that can leak "fluid" into the transmission. That would be the rare case where there is a hole in the transmission cooling line which usually connects into the radiator for the engine coolant to cool the transmission fluid passing thru the trans cooling line.
If a hole/crack developed in the trans cooling line inside that location, antifreeze/coolant could leak into the trans line.

Is the trans fluid on the trans dipstick normal colored, or does it appear to be milky with water/coolant intrusion?

Those are the transmission fluid cooler lines-one is the pressure line, other is the return line-back into the transmission. Often the cooling reservoir is built into the radiator. Apparently yours has a separate cooler in front of the radiator. It would be that and not the a/c grill.
Automatic transmissions generate a lot of heat. Without a way to cool the transmission fluid, the fluid could get burned-it will look blackened, and is very bad for transmissions. Check your transmission fluid and add if necessary. Stop the leak-it may just be a loose fitting, or a broken line or hose.

Radiators on automatics have a separate reservoir for transm. fluid cooling purposes. Didn't you remove the transm. fluid cooling lines from the radiator-a feed line to the radiator and a return line from radiator to the transmission? They are small steel lines that connect on the end of the radiator.

Is it a automatic or standard if it is an auto.I would check the modulator valve on the trans,pull the vaccum line off and check for trans fluid in the line.

I take it that it is an automatic transmission, if it is draining that much fluid a month and you can't find any outside leaks it could mean there is an internal leak somewhere. If you see a pink milkshake color in your coolant then it could be the radiator transmission cooler which I believe wont cause an outside leak so you can start from there. It is located and is part of the radiator. Just follow the transmission cooler line and it will lead you the possible problem.

IF TRANSMISSION LEAKING WHILE RUNNING LEAKING AT TORQUE CONVERTER SHAFT SEAL OR TRANSMISSION COOLER LINES GOING INTO RADIATOR LEAKING.YOU WILL LOSE MORE FLUID AT COOLER LINE BECAUSE TRANSMISSION UNDER PRESSURE THE OIL PUMP PUMPING IT THROUGH THE RADIATOR YOU WILL LOSE ALL YOUR FLUID QUICKLY IF LEAK COMING FROM COOLER LINES GOING INTO RADIATOR.DONT DRIVE VAN UNTIL FIX BECAUSE FLUID LOST WILL BE TRANSMISSION LOST.

CHECK UNDER VECHICLE IF TRANSMISSION FLUID UNDER TRANSMISSION MORE LIKELY PAN GASKET LEAKING FLUID.IF FLUID HAS NOT BEEN CHANGED THE PAN GASKET GET HARD LEAKS FLUID.THATS IF YOU HAVE SLOW LEAK.IF YOU LOSING LOTS OF TRANSMISSION FLUID ITS .LEAKING AT TORQUE CONVERTER SHAFT SEAL.LEAKING AT COOLER LINES.CHECK COOLER LINES FROM RADIATOR TO UNDER CAR WHERE COOLER LINES GOES TO TRANSMISSION. AND CHECK LEAKS AT FRONT DRIVE SHAFT AXLES SEALS

There are two possibilities
Either a bad gasket or the fluid internal pressure is too high due to bubbles getting in formed. if its gasket problem then the gasket needs to be checked.but if its high fluid pressure then bleeding the old fluid and refilling the new fluid properly will solve the problem. Also check How bad it is leaking? You certainly don't want to run a car with low transmission fluid as it will surely do internal damage. Most common leak areas are at the pan gasket or the transmission cooler lines that go to the radiator. Next most common areas are at the output shaft seals and around sensors or plugs on the transmission. If you replace any cooler lines with hose, make sure you use transmission hose. This will handle the pressure and the chemical resistance that other hoses will not stand up to. Also be sure to KNOW what transmisson fluid is needed. One size does not fit all! This will help. Thanks please keep updated.please please do rate the solution positively .thank you for using fixya

I don't know where your leak is happening but I suspect the transmission fluid attacks rubber and may be leaking from the heater because of softened hoses.
I think the first move I would make is to buy a Haynes or Chilton service manual and spend some time researching how the transmission and cooling systems are related. The books are available at auto parts stores (or on line of course) and cost between $17-$30 US.