Why does my MacBook Air randomly shut down on battery power?

I replaced the battery and thinking the logic board might be my next step. Currently, my MacBook runs fine when plugged into the wall, but quickly shuts down when on battery power. I can power it back up on battery power, but it shuts down again in roughly 45 seconds. I can't get any mobile work done without an outlet around.

Thoughts on replacing logic board? Reinstalling operating system? Thanks.