I have a 2013 that we just finished towing on a 9 week, 7000 mile trip. I installed the kill switch that kills the radio and did the upgrade to a larger battery. The upgrade requires buying the Honda Oddesy battery box ($13.00) and going with a Group 27 battery. The battery in the 2013 CRV looks like something that belongs in a motorcycle.
With the above mods, the Honda worked flawlessly for the entire trip with a couple of 450 mile days and no batteyr issues.
I also bought a non chipped key from Honda, which performs all the functions needed for towing, but won'yt start the vehicle.