Reopening recent files from photoshop home page

That's right. I use that same trick.

Cloudman's last post confirms everything I said. I don't know what else to say. You must pay attention to where you save. If a file/folder is moved or deleted, the recent file list will just contain a blind pointer.

Everythng that D_Foss said is exactly right, but here's a workaround that I've used when I wasn't paying as close attention as I should have been and "lost" a file due to Photoshop's seemingly random folder selection:

I simply load up another file - any file - and  do a "File / Save As"... this time, I watch where Photoshop wants to save this file, and sure enough, the "lost" file is right there as well!

By the way, Photoshop's folder selection is never random... it just seems that way sometimes when I'm working on more than one project and I get ahead of my skis.

The default location in Windows is the system "Documents" folder. Start looking there.

Generally, this is one of the reasons I think the home screen is a very bad idea. The recent file list is not a direct link to the file, as it is in a proper file browser. Instead it just points to the location on disk where the file was originally saved. If you later move or delete the file, the recent file list is not updated. It just keeps pointing to the same but now empty spot.

You must keep track of where you save the files. The way to do that is to use "Save As", where you get the folder tree to navigate in. If you just hit Save, you don't know where it's going. By default it goes back to the folder it came from, but it can also go to whatever folder you used last (depending on preference settings).

Use a proper file browser to navigate your folders. Windows Explorer is OK, but Bridge is even better and comes included with your Photoshop subscription.