@Pushkar Interesting outlook but I'm not sure I concur with your diagnosis.
The BT module is at the end of the board and is also laminated to the FR4. This should provide a lot of strength in flexion.
If the board is flexed, the middle should be the issue as it will undergo the most flexion. We thought of this and put the battery holder along the middle to give it more of a spine.
The middle is where the power circuit is located. It could be that one of the solder joints on those chips is loose and why you are getting some intermittent connections.
The pinky buttons are at the end of the lever but are supported by two tabs on the other side of the board. When in place, there is pretty much no movement in the board to cause noticeable flexion.
I think what you are seeing could be a loose solder joint on an important pin or pins.