Not aircraft or engine specific but..
In Canada we used to burn Jet-B.
With the demise of Jet-B we were obliged to use Jet-A or A1.
It became normal, on occasion, to have a flameout on the first start of the day on a "Cold Soaked" helicopter which had not been preheated.
Wait a minute or two and restart...no problems for the rest of the day.
I miss Jet-B.

As Helilife100 has said, the 'auto re-start' on a TU130 modified engine is most frequently triggered by air in the fuel of the HMU system during start.

There can be several reasons for this:

The most common I encounter is if there has been a maintenance action that disturbed the HMU fuel system prior to the start. For example, the HMU has been removed/refitted or replaced, the fuel filter has been replaced, or sometimes if the main fuel line has been disconnected for a supply tank de-fuel.

As Helilife100 stated, if the HMU splined drive shaft seal is leaking badly (lots of fuel in the plastic drain tube), air can find its way into the HMU. The seal can be replaced in a couple of hours.

A known problem is also air leaking past the seal of the metering valve cover on the HMU. This can be rectified by SB 319 73 2838 which introduces an improved seal and cover. Again, the HMU doesn't have to be sent away and can be fixed in a couple hours.