My daughter has a 2006 PT Cruiser that is having a overheating issue. Hoping you guys can provide some troubleshooting guidance.

After driving for approximately 30 minutes it will overheat. When it overheats, the car will shut off completely with no warning. After a couple of hours it cools down enough to start and add water. It usually loses over a gallon of water. There is no evidence of antifreeze leaking or on the ground. Currently it just has water in it as she's been adding water to drive it. She had it pressure tested today at a garage and they said it was fine. Fans checked out ok. There is no evidence of antifreeze in the oil.

Suggestions on troubleshooting it?

If it's losing coolant but not on the ground the only other choice is a head gasket leak and its going out the exhaust....

Yep,
Did one for this exact issue last year.
ROYAL PIA job by the way

Look REALY close on the pass side of the engine towards the front of the car, just below the area where the thermostat hsg is located.

That might not show up on a cold engine pressure test.

Change the thermostat.. simple things first
and a lot easier

First, check for combustion gases in the coolant which will tell you if you have a head gasket problem. There are a number of ways to do that. Do an internet search for your options.

Second, the fan has two speeds and it is very common for the low speed to go out. I have changed a bunch of them. In fact, it is common enough, that it would be a good idea to go ahead and change it.

And it is the fan motor itself that fails and only on the low speed. Not the relays. So, the fan assembly must be replaced.

It is possible now that the PT will have both problems. The fan problem leads to overhead problems, which kills the head gasket. As with many iron block, aluminum head engines, the PT's 2.4 is not tolerant of overheating.

IF, it going out the tail pipe, you need to fix it now. I had the same thing on my Neon, kept losing water, and I could even hear it gurgling back into the overflow bottle, and could smell anti freeze coming out the exhaust pipe. What was going on was the gasket working towards braking, then all of a sudden, all of the water will go out the tail pipe, and leave her sitting when the gasket lets go.