It is probably a Honda issue. On our 12 CRV, (virtually the same as 13,14s) the battery would be dead after not using the car for 3 or 4 days. This was before hooking up the charge line, only separate bulbs in the tail light fixtures.
In there effort to improve fuel economy, Honda reduced the output of the alternator to 12.1 volts, and using a small 400 amp battery to save weight. The battery was just slightly bigger than the battery for a small lawn tractor. After Honda replaced 4 batteries in the first year (all warranty), they finally reflashed the computer to give an output of the normal 13 volts. When the Honda battery gave up again, I put in an Accord sized battery, 600+ amps instead of 400. Had to change battery box to the Accord size, it fit perfectly. Even with the 3 yr old battery and our cold winter climates 0 F., I've let the car sit for 2 weeks and it would start no problems.
If you have the small 400 amp battery, cheapest option would be to put a trickle charger on it.
Ken