Yup. I've changed batteries twice. The car does wake up and respond at approach. My dealer recommended keeping the key out of range. It might help a battery that isn't brand new. I was having trouble finding the correct size battery locally. My brother in law who is a ASE mechanic suggested the Walmart battery. It's been way better than the OEM and saved me money. Just check the manufacture date to make sure it's fresh.

 

Are you sure the car wakes up 'on approach'. On mine as you start to pull the door handle it checks that key fob is in range and if so unlocks the door. But I can't believe it's constantly searching for the key fob when parked and locked