Linea Classis MultiJet Diesel Ignition key Issue

I am experiencing a weird problem. Once in a 2,3 months my Linea Classic MJD ignition key starts going blank suddenly. When I switch off the ignition and try to start the car, key turns completely all the lights on panel blinks and goes away as happen in noramal circumstances but engine doesn't get start not even cranks.
Than after waiting for 10 -15 minutes or 30-40 tries it get starts.
And problem problem persists for 1 or 2 day every time I turned off the engine I tries to start. After one or 2 day problem goes away and car get starts as normal. After 2,3 months again it behaves the same for a couple of day.
this problem got started 6 months back . A months before engine starter motors was got damaged and I replaced it.
After replacing motor this is the first time again it's having this problem.
Before motor replacement had a same issue a couple of time.

Is it any safety feature of car or any issue ?

 

I faced a situation similar to this.

Car, after running for some time, if stopped, would not start immediately.
I may have to 'cool down' the car for some time. May be 10 minutes or may be more. Then it would start.

I do not remember clearly how it was solved. It is still not solved for me. Only partly solved.
That 'part' is by replacing the starter and repairing/refurbishing the alternator. Now the car starts in first attempt or 2nd or third. Rarely it goes to 4th. Good thing is that, I do not have to 'cool down' between attempts.

I am asked by an FNG mechanic to check the 'high pressure pump'. I have not done yet, as the car can start in a few attempts.

Not sure if it can help you. @Athar

 

I have changed the starter moter. Now will look for alternator.
Thank you