2010 HHR SS. When purchased the vehicle it came with one fob. It only worked from the front bumper driver’s side to the driver’s side rear door. Installed a new battery. Same thing. I purchased a new factory fob and they programmed it. Same thing. My assumption is the antenna in the car has issues. True? Is there a part I can replace to improve the range of the fobs and its location? Thank you.

 

Mine works as you described. Up close, no problem when you push and release a button on the remote.
Now. What I found is if I'm any distance from the car (up to about 100 ft) then I have to hold the fob button down for an extended time. About a full 1.5 secs. seem to work for me.
Try that and see if it helps.

 

Try the old under the chin trick. Some say it works.
The receiver is under the bump in the headliner near the mirror.