But if it was something sudden, there should be something to find in the area that the transponder ceased functioning.

A simple automated (and non-tamper-able) spot tracker mounted in the tail or a cabin top pod would resolve all of these questions with about 10 minutes of work. I still can't believe we don't have this ability.

Cell phones wouldn't work out over the open ocean so even if there was time to get a call or text out, they would have had to use the plane's data systems to get it out...clearly those either weren't working or stopped working rather quickly. But, that does bring up another point...if there were a runway large enough to put that thing down, there would probably be a cell phone tower in reach and someone would get some sort of signal out. It's unlikely that plane is hidden somewhere.