heliski22,
Could just be that you're getting enough of a voltage drop during start for it to kick offline. Do you have 40 or 44 amp hour main battery, and 13 or 27 amp hour aux battery? The bigger aus battery certainly gives you more time before everything goes black!
I probably would have swapped the MCDU's side to side to confirm the problem before replacing it, but perhaps your mech's did that first anyway.
I haven't seen this problem much, only once or twice in the last year, but then we always start with a diesel powered GPU when we can. Resetting the CB, as you have found, normally fixes the problem.
Try dimming both PFD's when you're going to do a battery start. You don't need them during the start, and they actually suck quite a few amps.
You could also dim the MFD of the pilot not doing the start, just to save a couple more amps.
Anything you can do to save an amp here or there will help the start.
You might want to consider pulling the CB for the standby horizon as well.
We found that battery starts seemed to make them crap out after a while, and they are very expensive if not on warranty and also ground the machine until a replacement comes in.
After frying 3 or 4 of them, we wised up and pulled the CB.
Once the engines are started, then push in the CB while you do the post start checks. It'll be aligned about the same time that you are ready to go.
The manufacturer (Goodrich??) was supposed to introduce an improved version, but I don't know if they have or not. Haven't seen many battery starts for a couple of years on 139's, so don't know if the problem is still out there or not.
Sorry I can't be more helpful. Apart from low voltage, I can't think what it could be.