What else could be wrong with my Mazda Tibute 2008?

Sometimes it will start cranking then all power dies then all power comes back on then it
finishing cranking and starts (all in one turn of the switch). I've had the battery replaced,
replaced the ignition switch, had the starter checked out which they say is fine. Now I
don't know what else to replace, check or anything. And everything that's been replaced
has been checked out to be fine . I've been to different mechanics for second options and
testing and they all say everything's good, that's been replaced.