An acquaintance has asked for help with this issue. The dealership says the vehicle is fine, but the acquaintance has had the vehicle shutdown on her more than once, while driving. Usually while driving slow (<20 km/h), but the latest occurance was at higher speeds, which scared her good (it's a big heavy SUV that suddenly has no power steering).
I haven't looked at the vehicle yet (the Merc dealership took 6 days to not find anything), I should have my first look tomorrow. The vehicle can be started up after it shuts down by itself, so to me that rules out alternator/battery issues.
Sometimes it takes multiple tries to get it started, but the unsuccessful attempts don't make noise (the engine isn't turning over). Coupled with the intermittent nature of the issue, to me this suggests either a poor electrical connection, or the pushstart button is on it's last leg. Somebody suggested checking the fuel pressure as well.
Any suggestions for other causes? It's a diesel engine.