This is also happening to my Mazda 3. The weather us nust cild and not freezing, also when i manually unlock the door and try to start the car with the oush button it dies.not work until after about a.minute of trying.
my battery is wirking fine too.

 

same here. Live in San Diego so not cold but cool. Remote doesn’t work, key opens door but ignition button does nothing.
after many tries and locking and unlocking doors it usually works but takes about 5 minutes.