Could be any number of things - need to get a bit more information:
- Automatic or standard transaxle?
- Does it always fail to run after the second time is was started, or does it do it randomly?
- When you said it won't start, do you mean the engine will crank fine but not run?
- Has dealership ruled out a transponder key issue (ie, a problem with the ignition switch reading the key itself) - assuming the dealership even brought this up, if the car is so equipped?
- Distance to you destination is only 4 city blocks? Does the car show this weird starting behavior on longer trips?
My take on this issue - sounds like, even with an engine heater, the car is not run enough to get into "closed loop" mode - still in "open loop". This means the car will use preset engine parameters that enable the car to start and run until it gets up to operating temperatures and then optimizes the engine parameters with various sensor inputs. Very possible that the car was flooded with gas on the second start attempt and will be very difficult to restart. Hence by the time you get back to the car - the excess gas has evaporated and the car will start and run.
A couple of things to look for / try next time. Do you notice a heavy gas smell when this happens, or at any other time, other than while filling up the tank (EVAP issue)? When it drops into this no running mode but is cranking well - try pushing the gas pedal to the floor as you are cranking the engine. This will open up the butterfly valve in the throttle body and allow the engine to get more air - helps to displace/offset the excessively rich mix. Could be a ECU issue - unlikely, but possible. I would save that for the end - as the dealership is likely to stick you with the bill if you are out of the powertrain warranty period (60 months / 60,000 miles). An xpensive part - looking at atleast $950 - $1500, depending on the dealership.
Good Luck.