This may sound dumb but I do not mean it to be insulting. Go to a auto parts store and have the transmitter check. You hold it within a couple of inches and press. If the light goes on their instrument it is transmitting. If not check that the batteries are in correctly. Any dealer also can check this.

Another thought the key and lock work off the CAN bus via the chip in the key which is tied to the VIN and the automatic lock/unlock uses an automatic transmitter which then signals the CAN bus. IF one key works and the other does not it has to be the batteries OR the transmitter in the key. If the batteries are OK then the only solution is a NEW key. They run about $130 from the dealer. You will need VIN and proof of ownership before they will order one.

One other thought watch where you stored the spare. It can be damaged if in a junk draw. I keep mine in my night stand draw.