I doubt the antenna as well, but the static discharge is what damages the module. Either way.
Do you always have to reprogram it after starting?
You only pay when you accept my answer.
There is a bulletin for this. I recommend you replace the module and remotes, then program the system. Below is the bulletin.
#06-08-52-002G: Remote Keyless Entry (RKE) Inoperative, Poor Range, Tire Pressure Monitor (TPM) Message Displayed, Remote Vehicle Start (RVS) (Replace RKE Transmitters/Reprogram Remote Control Door Lock Receiver) - (Nov 24, 2008)
This bulletin is being revised to update the Part Information. Please discard Corporate Bulletin Number 06-08-52-002F (Section 08 -- Body & Accessories).
Some customers may comment about one or more of the following conditions:
The remote keyless entry (RKE) transmitters will not program, function and/or the RKE transmitter low battery message is displayed.
The Service Tire Monitor System message is displayed.
The new RKE transmitters cannot be programmed.
The remote keyless entry (RKE) and/or remote vehicle start (RVS) transmitter has poor range.
Any of these concerns may be caused by an internal fault with the transmitters and/or the RCDLR software/hardware.
Important: Check VIS to determine if Inventory Upgrade 07007 applies and has been completed. If the vehicle is listed in the Inventory Upgrade, and the upgrade has not been performed, complete the Inventory Upgrade before proceeding with this bulletin.
DO NOT REPLACE THE BCM OR RADIO ANTENNA MODULE.
Complete the following repair procedures:
Important: When programming a new or existing RCDLR, the programming instructions in SI must be followed.
Important: If the Inventory upgrade 07007 has been performed, skip the initial RCDLR programming step #1 and proceed to step #2.
Important: New transmitters are identified by a star on the back of the transmitter. It is important to verify that the replacement transmitters have a star on the back.
Important: In most cases, steps 1-3 will correct the customer's concern. In a few cases, it may be necessary to replace the RCDLR.
Important: Refer to the parts catalog to identify the correct part numbers for the vehicle being serviced.
Transmitter -- 5 Buttons with Liftglass, Power Liftgate and Remote Vehicle Start System
Transmitter -- 3 Buttons with Remote Vehicle Start System
Transmitter -- 3 Buttons
Transmitter -- 5 Buttons with Liftglass and Power Liftgate
Transmitter -- 4 Buttons with Liftglass
There is only 3 wires to the module, power, ground and the network. This should not go to sleep. It this was mine, I would try to flash the system with the newest calibrations first and try.