Maybe I was unclear but I was referring more to the solution suggested than the problem that guy had:
"...the problem of starting on the second try is normally because the fuel pressure has bled off the injector rail while the car sat. The check valve (normally in the outlet of the fuel pump) is supposed to keep the pressure up for many days but a leaky check valve or dripping injector can bleed off the pressure in minutes. When you crank the first time the fuel pump runs to restore the pressure, and when you crank again it is ready to run. I'm not familiar with the Mazda, but most cars will also start on the first crank if the ignition is left in the "on" position for a few seconds (like 2-4 seconds) before cranking if the pressure has bled off."
I am going to monitor times between the failures.It seems that issue happens only if some time has passed that correlates with the explanation above.Also I will try to leave ignition in 'on' position as suggested above first thing in the morning.