I had the same issue.
Here was my post about it:
http://ducatimonsterforum.org/index.php?topic=6561.0It boiled down to two problems for me: idle speed too low AND, this is the big one, throttle bodies were OUT OF SYNC from the factory. Typically, bikes quitting when coming back to idle, especially after down shifting
Since adjusting both, haven't had a problem.
With regards to the battery, the voltage read out through the gauge cluster is actually very accurate. So, if you're suspicious of the battery, check the voltage both cold in the morning before starting, and after starting the bike. Should be around 12 to 12.4 in the morning. 13.6 - 13.8 after starting.