Transponder battery?

FOB battery should not be draining when not in use as there is no contact of components to cause the draining. If FOB is kept in pocket of tight jeans etc, there is a possibility the buttons are being depressed most of the time causing the draining. Other than that I cannot think of any reson for the draining.

As to the headlight bulbs, a good quality bulb should last but those of inferior quality might not last and is likely to blow when subjected to usage and vibrations.

Check out the diagrams (Below). Please let us know if you need anything else to get the problem fixed.

Need to reprogram the remotes.

If that doesn't work,

Power lock circuits usually control the action of a solenoid or motor. The movement of the center core of the solenoid controls the action of the lock levers and arms. The movement of the motor causes causes the lock mecanisme to operate.
The best way to diagnose a power lock problem is to refer to the wiring diagram for the circuit.
If none of the locks work, suspect an open to the control switch.

When you don't use the remote, do the door looks function normally, quietly, and powerfully? If the answer is yes and temp etc makes no difference, I would suspect the control module for the remote. I suspect that when the car is now warm the remote works fine say after driving and warming the car. The temp then of module is elevated to the vehicle temp and warm it will work. The modulator has a couple of relays built in and they will sometimes get weak.

If what I have fits what you are experiencing, I offer three options, one replace the module with a new on from Honda, do nothing and it will get worse, or purchase and either install yourself or have installed a remote car starter w/remote lock. I have installed in my vehicle and get better range from the remote with a third party remote start kit and the cost was just under $100 with me doing the work. In fact, I have installed now two of them.

When you press the button, does the led lights up?

You can try to reprogram the keyless remote.
* Turn the ignition switch to ON, within 1-4 seconds press the keyless remote lock or unlock button.
* Turn the ignition switch to OFF.
* Turn the ignition switch to ON again and within 1-4 seconds press the keyless remote lock or unlock button.
* Repeat the top procedure for one more time.

When you hear the door lock cycles during programing just press the keyless remote lock or unlock button one more time and then remove the key.