Replacing the rim tape will fix the problem only if the current tape has slipped and exposed a sharp spoke hole or valve stem edge.
Blow the leaking tube(s) up very firmly (they should look like sausages) and then dunk them in a bucket of water. The leak may be very slow but you should find it if thetube is presurized adequately. Then notice where it is relative to the rim and whether it faces the rim or the tire.