I have an 05 Malibu with the radio antenna embedded in the rear window glass (above the defrost elements). The antenna connects to the radio via a "button" (more like a snap) that is attached to the glass and a wire that comes out from under the roof liner and attaches to the button. That then feeds a signal amplifier that is in the back somewhere. I noticed that the AM reception on my radio had gone to crap and after doing some detective work, saw that the "button" on the rear window had come off the window. It looks like it was soldered on, but I have not been able to re-solder it. I've resigned myself to adding a new antenna, and since the antenna lead is in the roof line, I'm thinking of a European-style roof antenna.
Does anyone have any recommendations, or other suggestions (I really would rather not install a fender antenna if can avoid it).

You might try using the repair compound used for fixing rear window defogger heaters. It's called Quick Grid and is made by Permatex available from auto parts stores. It's conductive and I would put a blob on the detached button and fix it in place with tape until the compound had set. Clean the area with isopropyl alcohol first. It's worth a try but I don't guarantee it will work.

Back in '03, about a year before I traded my '98 LS for my current '04 Maxx, the rear defroster connection on the drivers side had detached. I tried all of the "fixes", to no avail. Fortunately I was still under GMPP and the solution was to replace the rear glass, which seemed drastic, but it was free.

I've had a look at my Malibu and the antenna is printed on the inside surface of the rear window. If you run your finger over it you can feel it. So I think it's quite possible to attach a connection to it using the compound I mentioned above. There is no heavy current flowing in the antenna like the defroster heater so it should hold. There is approximately 2 inches of conductive print that can be used as a connection. Just in case the original connector broke off and removed some print.

Thanks for the tip, Jetex. I'll give it a try!

I tried the Quick Grid fix, and it worked fairly well. Definitely an improvement, but not to where it was before. My guess is that the Quick Grid glue doesn't have enough conductivity for the very low radio signal that has to pass through it.
I pulled the headliner down, and removed the amplifier that is attached to the roof and pulled the antenna and power leads into the trunk. I'm just going to go with a fender mount antenna near the trunk and call it good. Certainly a lot cheaper than a new rear window!

I'm sorry to hear that it didn't work too well. After talking to you I made a pellet of Quick Grid about 1/16 of an inch thick and 1/4 of an inch wide (the leftover stuff in the bottle had got a bit thick) and, after letting it set for a day, took a resistance measurement across its thickness. I came up with about 0.4 ohms. After reading your post today I took the pellet and measured it again and came up with 00.0 ohms. So it seems as if the resistance goes down as the stuff dries out. That's the resistance across 1/16 of an inch with the meter probes held flat across the two surfaces.

I hope your problem is not further along.