I believe they should just cross out the "normal" circumstances and start thinking backward.
Normal circumstances, radio communication and radar will always be on. Now if they can't communicate with the plane for an extended period, they should start to look from the last received transmission, calculate the maximum possible radius distance, start from there and spread out.
It's not the most efficient ways, but surely with today's technology and several nation's working together you can really pinpoint the area of crash faster, instead of coming up with no explanation at all?
And FWIW, It must have been a crash, and the passengers would presumably have deceased (or they could contact their family), we don't have anything too savy for conspiracy theories at the moment, it could be terrorist or hijacking or any other espionage plot, but as of now... I don't think anyone have the tech to make a plane simply disappear. It's probably a simple but extraordinary coincidences of things (Pilot having a heart attack, thunderstrom turning plane electricity out, etc). Surely there's no alien involved.