Do they stay until the tab is restarted?
Are you running a battery saver or memory saver app?
Are you running a launcher or widget app?
Is it all of the apps you've moved to SD, some of them, or just a couple of them?
If you move one of them that has disappeared back to internal storage will their icon stay on the screen then?
This was a classic issue with apps to SD when it started on older devices, honestly I haven't heard of it happening in so long I'd forgotten it was ever an issue. In the past what would happen was like a delay but the items would eventually return to the home screen. So the device obviously pulls from its internal memory first then from the external memory, the SD card. I can actually watch this happening on my old Rezound. If I open the app drawer, I can see the apps being loaded from the SD popup one by one as it scans the SD. I don't have many apps on the home screen, most are in folders but I can see it in my folders as well. With the updates to today's devices though this should be a thing of the past. Even if the device is older the new OSs should have addressed this issue. Do the missing icons ever show up or not at all? The reason I ask is because I'm wondering if it would show up if you went into your app drawer and opened the app. See it sounds like you may have a battery saver, or memory boost app running that only allows the device to open items as needed or requested. So let's say your Chrome icon isn't on your home screen but you open it from the app drawer, now you've initiated the app so it is running/active and now it appears on your home screen. Because it is not an essential app for start up your battery saver, or memory saver app may not let it start. Try disabling it if you are and see if the issue doesn't stop.
If you're not running anything like that or they don't appear even after you've opened them, my next thought would be a launcher or widget app. Check your launcher for something that might allow you to lock and unlock icons. I remember reading about one that allowed you to place anything you wanted on the home screen until restart. Once restarted it gave you a clean slate to start all over again. I guess the feeling behind that was what you are doing day to day changes your home screen can change with you, and things you needed yesterday you may not need today and so on... Although I thought you could lock icons to prevent this.? I mentioned a widget app only because it would affect items on your home screen, even though I didn't think it would remove items the two are kind of linked. Disabling either of those or uninstalling them just as a trial to see if the issue stops would be worth a try.
Beyond all of that I have no idea. I would say place the items in a folder and see if they disappear from there, or if the folder disappears as well?