4 out of 10 times, the doors won't automatically unlock when I come near the driver side door with my key fob. Is this a known issue with the GT? If it's not a known issue, could it be that the battery is dying in the remote?

So every time I put up the fobs I click them twice to deactivate radio And save the battery. As a result, when I walk up to the car there is no automatic opening as the radio was shut off so you have to click the fob again.

The problem I’ve been having more is that the car doesn’t recognize when the key is in the cockpit to start and sometimes I have to manually start it through the Glove box.

So you're saying you can disable the radio by clicking "lock" twice? If so, that may be the reason why automatic opening doesn't work half the time for me haha

The double click is a good idea to prevent auto theft as well. I do it all the time. Thieves have access to some devices that allows them to extend the signal range and trick the car into thinking the key fob is nearby. They simply open the door get in and drive off.

Sounds like a key fob battery issue to me. Why not spend a couple dollars and just replace it. Easy to do yourself and can buy the batteries anywhere, target, walmart, walgreens, etc. The battery in my remote is CR2025

My problem is that my car doesn't lock automatically when I walk away. I've just been using the key fob manually. Yes I have aotomatic locking turned on.

Same problem.