This is a model S isn't it?
If memory serves there is a position on the front windscreen to place the fob when batteries are low or not working - base of passenger side windscreen wiper and then press door handle (might be passenger door handle?). Likely will have to try both sides if the instructions apply to US cars.
Failure of aerials can contribute to poor signals too .. so if usually car/phone is linked by home internet but you have good phone signal strength then try turning off phone wi-fi or turning off phone cell connection when trying the app?
A while back i did post a msg about changing my fob batteries for some I had lying around (new in packet) that failed to work - but it was fine when I bought a better brand - obviously the first lot had been sold as old stock and then sat at home for more months.