Problem with the range for controlling Sunset Cruiser 8676
I had a 8378-1: Red Beast RC (which is practically the same hardware aside from running on a different frequency) that developed a similar problem shortly after I got it. One day the receiver only worked if the remote's antenna was about 2 inches away from the receiver's antenna.

I got it replaced, and it was indeed the receiver and not the remote with the problem. I later tried taking the busted one apart to see if it was something obvious I could re-connect, but nothing stood out as being broken.

Unfortunately, I think your problem is hardware failure. I don't know of any easy fixes, but would love to be proven wrong on that.