iPad screen flickers black when device is touched

My iPad Air 4 has started flickering and going black when I touch the casing. Mostly when I touch the back of it, such as to pick it up, or the outer edge, such as to steady it when drawing. Sometimes it flickers back on immediately and sometimes it stays black. It also doesn’t seem to like the Home button being touched to wake it, and sometimes it starts blacking out when I’m typing. As you can imagine this makes it almost unusable.

Pressing in the centre back of the iPad stabilises it for a little while, then it starts again. I had this issue before and both times it had been after I’d taken my iPad with me on a long car journey (where it had not left my backpack by my feet the whole time). Everything is up to date and I’ve done all the restarting/charging stuff. It definitely seems to be a hardware issue. Has the motion of the journey jostled something loose? It’s in a protective case and has been since I got it 4 months ago, and there’s no damage to it whatsoever. It can’t possibly be that delicate!

The most frustrating thing is I reported it to Apple who arranged a repair, but as soon as they got it, sent it back because they “couldn’t replicate the fault”. I’d even sent a video of it happening. And now it’s doing it again, essentially whenever I pick it up to move it or touch it to use it.

Someone else must have had this fault and it must be fixable!