Ooh, that's frustrating!
That looks like it's a fuel-related issue or something with the electrical system!
I'd rule out the simple stuff first.
Make sure you've got plenty of fuel and that the cap isn't clogged.
Next, check for any air in the fuel lines, since a cracked line or loose fitting can let air in and cause it to lose prime.
You might also want to bleed the fuel system to rule that out.
If that doesn't work, check your fuel shut-off solenoid or crank position sensor.
You can also check for a clogged fuel filter, which can sometimes starve the engine and cause it to just die.
