If you have the Honda add-on system with Honda remote A269ZUA101, you can put the system into Valet mode. My BIL's 2001 LX also is having issues with the remotes and I just pulled out the manual a couple of days ago.
If your system is armed and you open the door and the alarm sounds, you can turn it off by putting the ignition in ON position and pressing the bypass switch they installed on the panel around the knees.
To put in Valet mode, you have to do the following.
Disarm the system and remove the key from the igntion. With the ignition OFF and system disarmed, press and hold the bypass switch for 5 or so seconds and the indicator light will blink confirming that the system is now in Valet mode.
To turn off the valet mode, repeat the steps when the system is in Valet mode and the indicator light will blink twice (I think) to confirm the system is now not in Valet mode.
** Edit **
Since I was nice enough to post the instructions, please don't compete with me on ebay for one them replacement remotes.