Loss of battery power in flight CAN happen! I have witnessed this failure myself in an MD-11, and
AFAIK it was caused by corroded or otherwise faulty connectors. An intermittent "BATTERY LOW" indication was the first sign that the system didn't work right; the battery voltage indication literally swapping between 28 and 0 Volts (no intermediate low voltage indications, so the battery charger was functioning fine). At first an indication problem was suspected, but when the captain's clock also failed it soon became clear that battery power indeed was intermittently (and later permanently) lost.
Now, I have taken a look in the MD-11 electrical schematics, and its DC arrangement seems to be quite similar to the B737 in that a 'Battery Direct Bus' (comparable to the 'Hot Battery Bus' of the Boeing) is powered either by the battery charger or by the battery itself. But since this diagram is even more confusing than the drawings in the 737 FCOM, I can't really figure out whether this 'Battery Direct Bus' indeed powers the captain's clock or if there is perhaps some even more direct connection not shown in the diagram, and I am also not clear where exactly the battery voltage is measured.
Anyway, the consequence of a "BATTERY LOW" warning is to land at the nearest suitable airport, which is due to the fact that this situation unpowers not only the captain's clock but also the fire bottle squibs. Due to the similarities in design I wouldn't rule out the possibility that this problem can occur in a 737 also.