I've been having a similar problem. I have to practically be on top of my car for the remote to work. I sometimes get the message about servicing the tire pressure system, and I think that's somehow tied in to the hesitation problems I have as well.

 

There's a service bulletin on this issue

HERE IS THE SERVICE BULLETIN I FOUND PARTICULAR TO '06 AND SOME '07 IMPALAS, KEEP GOING DOWN AND YOU WILL SEE STEP-BY-STEP INSTRUCTIONS:
Bulletin #: 07-08-52-001C

This may be the one that also includes the Monte's as they use the same parts ... but there's one that does include the Monte's

Subject: Remote Keyless Entry (RKE) Inoperative, Poor Range, Tire Pressure Monitor (TPM) Message Displayed, Remote Vehicle Start (RVS) (Replace/Reprogram RCDLR, Replace Antenna and Transmitters)

Supercede:
This bulletin is being revised to update the Parts Information. Please discard Corporate Bulletin Number 07-08-52-001B (Section 08 - Body and Accessories).

Condition

Important
This bulletin does not apply to vehicles built after the following dates: - DTS / Lucerne: 5/1/07
- Impala / Monte Carlo: 3/1/07

For vehicles built after these dates, refer to SI for diagnosis and repair information.

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 transmitter cannot be programmed.
- The Remote Keyless Entry (RKE) and/or Remote Vehicle Start (RVS) transmitter has poor range.

Cause

Any of these concerns may be caused by an internal fault with the transmitters and/or the Remote Control Door Lock Receiver (RCDLR) software/hardware.

Correction

DO NOT REPLACE THE BCM.

Important

- The 2006 and 2007 Impala LS without AP8 does not have a coax antenna.
- The 2006 and 2007 Lucerne without AP3 or AP8 does not have a coax antenna.

1. Replace the RCDLR module and the RCDLR antenna using the following procedure:

Impala / Monte Carlo 1. Remove the driver's side "A" pillar molding and I/P closeout panel.
2. Unplug the speaker.
3. To expose the RCDLR antenna, partially remove the driver's side upper I/P closeout panel (near windshield).
4. Remove the clips holding the RCDLR antenna wire at the RCDLR module and along the "A" pillar.
5. Cut the old RCDLR antenna wire a minimum of 152 mm (6 in) from the button (connecting to the windshield), leaving that portion of the old RCDLR antenna connected to the windshield.
6. Remove the I/P carrier bolt and remove the old RCDLR antenna.
7. Remove the RCDLR module.
8. Install the new RCDLR module.
9. Lay in the new RCDLR antenna and reinstall the carrier bolt.
10. Connect the new antenna to the RCDLR antenna module.
11. Clip the new RCDLR antenna into place using the existing holes on the "A" pillar.
12. Reinstall the I/P close-out panel.
13. Reconnect the speaker wire.

Important
Be sure that the end of the old RCDLR antenna is tucked behind the "A" pillar molding. The button on the windshield is no longer functional, however leaving the cover on the button will provide a cleaner look to the vehicle.

14. Reinstall the "A" pillar molding and I/P side closeout panel.