I've seen this in the manual, can't say I believe it, but I guess there are circumstances:
"NOTICE
When using a key containing a transponder
chip, observe the following
precautions:
When starting the engine, do not
use the key with a key ring resting
on the key grip and do not press
the key ring against the key grip.
Otherwise the engine may not start,
or may stop soon after it starts."
This is in the manual for the SmartKey, but I wonder if it's possible there is some comparable logic in the standard system? (I don't know of any folks leaving the key in the ignition, but it likely does occur. If you know it does not disable other Avalons then I'm probably off base. I do have a friend, however, that keeps an LS430 key inside his car all the time.

)
SmartKey:"Both the vehicle and key transmitters are
always sending signals to each other. To
prevent the batteries from being discharged,
the smart key system is automatically
deactivated in the following conditions:
If the electronic key is left outside of
the vehicle and within the effective
range of the entry function actuation
area for more than 10 minutes.
If the door lock or unlock operation is
not performed more than 2 weeks.
The key and the vehicle are communicating
even while the vehicle is not being
driven. Do not leave the key near the
vehicle (within 2 m [7 ft.])."
To reactivate the SmartKey you have to use a remote function or insert and turn the metal key in a door.