Sounds like starting it uses more power than the alternator can replace in the short distance you drive. It's a common problem. Also, as soon you turn the key, a bunch of electronics get active and they all pull from the battery.
I have an 2005 CRV... and that has been my opinion as well.
I use BatteryTender units on various things...
At $60 (IIRC)... I have been quite satisfied. From diesel gensets... Cummins trucks... CRVs... never a complaint.
