Internal SSD often not recognized, but working fine when recognized
I have a Macbook Air mid-2013 with a 256GB SSD drive. It was working fine, but one day after a long plane trip, I turned it on and it was showing the blinking folder icon with a question mark. I entered Recovery Mode and used diskutil to see that it plainly wasn't recognizing the main drive (it wasn't showing up at all). Resetting SMC and NVRAM didn't help.
After that, when I try to turn the computer on it mostly isn't working, but sometimes (like now) it works perfectly fine. I ran the bundled disk utilities and smartctl tests and everything comes out perfectly.
I took it to an official Apple store, who told me that the drive is broken and needs changing. That seems not to be the case, and I would not like to do that. A complete copy of the disk has been made, so I am not risking data loss (though I'd like to avoid having to format the drive). It would seem the disk is just fine, but the problem is somewhere else. I was suspecting that the SSD is loose or something like that.
What would you recommend? I was thinking of opening it up, cleaning it up, disconnecting and reconnecting the SSD drive, and hoping it would help. But before opening it up (something I have never done), I'd like to be sure I have exhausted all my options.
UPDATE: When I wrote the above the computer was working, I left it sitting for a while so it went to sleep, and when I tried to wake it up it wouldn't load anymore. I rebooted it and the folder with the question mark appeared again.
UPDATE 2: Here's the main screen of Coconut Battery 3.9.4: