What fuse number did you pull? I believe it should be 19.
I've not tested my lighter outlets because I don't need them with my Air Force One. Are you needing the power for your aux brake system?
Are all the lighter outlets dead? I'm thinking you have one accessible to the passengers.
If I had a system that required power to run I would probably opt for something like Toad-Charge.
LSL Toad-Charge Dinghy Vehicle Battery Charger/Maintainer 40' Wire Harness
That would be a good answer to ensure your CRV battery doesn't get discharged. My experience with my CRV is that the battery is not the deepest in power reserves and I don't even have the NAV system in it either. However, with the fuse disconnect switch I have had ZERO problems after a long day on the road but I don't have any need to use any power outlets while towing either.