The first thing I want to ask is if you checked for diagnostic trouble codes, but I have a feeling I may know what is happening.
The scan is a good idea regardless, but here is what I suspect. There were issues with the transmission cooler being restricted or plugged. Since reverse requires the highest level of line pressure, I have a feeling there is a blockage and causing reverse to fail.
Please understand this is a theory based on the idea that it happened all at once and all forward gears work fine.
If you look below, I was actually able to find a technical service bulletin related to "Mandatory Oil Cooler Cleaning." I attached it below. Note the first two pics were added to help you determine the inlet and outlet hoses at the radiator. The remaining pics are the TSB which explains how and what needs to be done. Note that the TSB is for multiple vehicles, so don't be confused. Additionally, the last pic shows the line pressures needed for forward gears vs reverse. Notice how much higher reverse requires. That is what my theory is based on.
If you suspect this isn't the cause, I would have the computer scanned to determine if there are diagnostic trouble codes related to the transmission.
Try this and let me know if it takes care of the issues. Also, let me know if you have other questions.
See pics below.
Images (Click to enlarge)
Monday, December 27th, 2021 AT 6:07 PM