If replacing the battery doesn't work, it could also be the keyless entry unit failing. I had my OEM keyless entry/security unit on my 2000 Civic crap out on me. I kept pressing the button numerous times before the doors unlocked/security disarmed. Then, one day, it just didn't work and I had to actually turn the key to open the door and disarm the security. Come to think of it, it was just the keyless entry unit then.
See if you can test the unit (or bring it to Honda and have them test it).
