If the remote start was at fault, it would act up when you use the remote feature. It could power up the ignition circuitry to get the car running, but if the trans power circuit does not power up untill you get in the vehicle and actually turn on the key, then it is possible.
Your car probably has 3 ignition power circuits that are all isolated from each other when the key is off. If the remote unit doesnt power up all of them, it is possible that codes could be generated and the trans could go into default mode.
Chances are that is not what is happening, although it is a remote (no pun intended) possibility.
If the problem occurs every time you use the remote start, then it may be the trouble.
If it happens without using the remote start, then the remote module wiring in question probably isnt the issue.
You can unplug the remote module, and then try it for a day, to see if the problem still occurs. That would help you rule it out.
It could be a wiring problem like I said, it could also be the wiring inside the transmission.
Fact is stranger than Fiction