When this issue started back up it did it on a daily basis, at least once a day (When I say daily basis, I mean every single time I drove it, sorry). I took the advise of Sean and secured my TwEECer very well to the computer. It was very loose before. It never fell out (if it does, the car shuts off) but it wouldn't surprise me if all the vibrations of this car (Extremely stiff chassis) was moving the TwEECer around enough to freak the computer out.
So, I secured it and have been driving the car for the past week (Literally every day to work and back) in warm conditions, freezing conditions, rain...etc. It has not acted up once. I'm not going to call the problem solved, as it will take quite a bit more mileage to confirm that was the issue.
Thanks everyone for their suggestions!
-Sam