I'm having the following issue:

I have a Screen layer, I want to move a part of it. I select said part with the Rectangular or Outline Selection Tool, then switch to move tool but when I click or move the selection it disappears completely. Furthermore, Ctrl-Z doesn't work at all after the selection disappears until I change from Move tool to any other. Then I can undo to make the missing part reappear.

I can move other selections without issues, it's just this one layer. This has happened before and I have to close Kirita and reopen the document for it to work again.

What is a 'Screen layer'? (I only know about Paint layers, Vector layers, Group layers, etc.)

When you Move a selection, it is possible that you will make many small moves in an attempt to 'get it right'. Because of this, krita does not record the move action in the history list until it is sure that the move has been completed. The only way it can know this is if you change from the Move tool to another tool. There are arguments for and against this behaviour but that is what is does.

"I can move other selections without issues, it's just this one layer." This may be because it's a 'Screen layer' and not any other kind of layer?

Can you post a full .png screenshot that illustrates this problem?

My bad, I mean a Paint layer set to Screen mode although I'm sure it has happened with Paint layers set to other modes or even Normal as well.

Here's an example of what was happening:
https://i.imgur.com/j80wVo7.png

As soon as I select the Move tool and click the canvas (even if I don't drag it anywhere, mouse completely still) the selection disappears. If I don't undo, it's gone forever as if I had deleted the selection. Everything else in the layer (the other cheeks and nose shine in this example) remains, it's just the selection that gets lost.

It doesn't look I can reproduce that. Could you please tell me the exact version of Krita you're using (Help/About Krita), whether canvas acceleration is on (Settings/Configure Krita/Display) and whether toggling that helps.

I'm using Krita 4.1.1 but I've had this problem before, since at least version 3 (with two different Windows 10 PCs, but the same Monoprice ScreenDisplay if that makes any difference). I'm unable to reproduce it either, restarting the program usually fixes it and it seems random whenever it strikes again which can be every couple of days or longer or shorter.

I had acceleration turned on, I'll turn it off now and post if it happens again.

Ah, I hadn't understood it was an intermittent problem.

"My bad, I mean a Paint layer set to Screen mode although I'm sure it has happened with Paint layers set to other modes or even Normal as well."

I still have 'terminology confusion' here. What is meant by setting a layer to 'Screen mode'? (Is it one of the blending modes?)

(EDIT: Ok, I found it, it's one of the blending modes in the Lighten blending group.)

As for the selection and the moving, when you select a region then it is outlined with the 'marching ants' dotted lines. When you use the Move tool, these lines are removed and replaced by a larger rectangular bounding box that is only visible during active moving and the selection dotted lines remain invisible until you change the tool or you can do Select -> Reselect (Cntrl+Shift+D). However, the selection is still active even if you can't see it.
(I've always assumed that this is to enable you to do fine positioning by removing the visual distraction of the dotted lines.)

Is this what you mean by 'the selection disappears'? Or, do you mean that the selection is no longer present or active in any way? Can you use Select -> Reselect to restore the selection dotted line indicators?

You did say that this doesn't happen on other layers so that seems to indicated that you mean the selection is no longer active in any way and the problem is limited to that one layer that you have set to 'Screen mode'. Screen blending mode.

EDIT: The blending mode shouldn't have any effect on Move/Selection since it is applied to the image layer stack rendering process. Please confirm that this is the case by setting the blending mode to Normal when you have the problem and seeing if you still have the problem.

Your screenshots are limited to a small region and do not show the Layers docker or the Tool Options docker. This information may be useful since the Move tool and the Selection tools have a variety of option settings that can be chosen for their operation.