Mysterious case: chain falling off large chainring, how to fix?
Yeah. A modern double chainring is ramped and pinned, in order to be more easily shifted from one ring to the next. Simply put, the chainring "wants" to pass off the chain to the next cog. Without a derailleur to keep it in place, the lateral pull of the chain shifting across the rear, combined with some road jostling, can make the chain fall off the front. 

A couple solutions: 


install a singlespeed chainring without ramps or pins, with "straight" teeth.  
use an outer chainring guard and inner "dog tooth" chain keeper  
combine the two (which is the best solution).


The free and easy way to keep it on while looking at other solutions is to reinstall the front derailler and adjust the limit screws so it keeps the chain in place.

This is a pretty common concern with cyclocross. Racers often use a single-chainring setup for the sake of reliability, and either or a dual chainguard or chainguard-and-chain watcher setup for just such reasons (also because they keep picking the bike up and putting it down whilst running and jumping over stuff), so you get stuff like this: http://www.bikeman.com/CC-SRAMS300CX.html.