I've had issues in the past with corrosion on the AAA carrier and on the small pins where it plugs into the circuit board on the tach. I've had luck cleaning those contacts.
If its deeper than that its be a matter of opening it up and poking around with a volt meter, following the circuit further from the battery to check continuity.. depending on your comfort level, obviously
I was told awhile back by AIM that if I had this issue to "roll" the batteries in the holder back and fourth to help with a better connection. It did work, but after a few races I had to remove the cover and do it again. The battery holders are no longer available new and hard to find good used ones as well. About 2 years ago I had two very nice Mychron 3's that I hoped to be able to find some sort alternative battery holder for but never did so I sold them off cheap for parts .