Precision 5510 bad SSD connection

Since recently I was experiencing a number of sudden random freezing of my Precision 5510 (with a 1TB M.2 PCIe Hynix SSD) every day followed by BSOD, which never led to a memory dump being created. On a few occasions during boot I got the message that the hard drive was not found. Every time I was however able to reboot successfully on a next attempt. I then noticed that I could trigger a crash by physical movement (gentle shaking, bumps or vibration) of the laptop, which leads me to believe there is a faulty SSD connection. Since then I have kept the laptop stable on a desk and have experienced no more crashes already for several days, proving my hypothesis that it is a hardware issue rather than a faulty driver.

Obviously my warranty just expired a few months ago so now I'm considering to open up the laptop myself to try to fix this issue (I have had some experience opening up laptops previously). Is it possible that these symptoms are caused by a bad connection of the SSD which I can fix myself? Or is it more likely due to a faulty motherboard which will result in a much more costly repair? Any tips are much appreciated before I start dismantling my computer.