4th time the charm?

I am guessing they installed a 6X9 speaker. At least that is what I am seeing as comes stock. You could adapt any smaller speaker like a 5 1/4 up to a 6 1/2 fairly easy.

Without knowing the exact set up I will suggest this, think about adding a dedicated subwoofer. something self contained with an amp like a bazooka or infinity bass link.

Here is why:
The GM audio systems pre 2007, have a volume dependent EQ setting that as you increase the volume (get louder), bass frequencies are attenuated. So now you adding an amplifier, and let's say they are running the 6X9's unfiltered you can potentially blow the speaker either thermally or mechanically. The sad thing is, it can happen quickly. especially the mechanically way. I suggest you get a multimeter and check the blown speaker to confirm if you have blown it or if there is a wiring issue.

If truly the speaker is bad which is strange that you continue to lose just one, I suggest just getting a reasonable cost 6X9 pair. Hopefully the amp has crossover functionality and high pass the them around 80 hertz to protect them. Then add your powered sub and call it a day.

I can suggest a lot of speakers that will fit. I need a budget that you want to work within.

Could you specify what is meant by when the 'back speaker will go out?' Does it not make anymore sound or is the bass rattling? Sometimes bass rattling is something else in the back shelf rattling. If it's out, then I'd just take it to another shop. Tell them you want to find out what's happening. Hopefully it's just a loose connection. Or it might be a bad connection meaning something is shorting the amp to the chassis. Best of luck.