Where exactly do you save the files? On the cloud , or on your computer. Can you see those files when you try to open the recent files?
or when you click on the house icon, top left
You can test and see if you see them when you click on "your files" (after clicking the "house" icon)
if you see them here, they are saved on the cloud.
Just in case, can you screenshot the window when you save? (assuming you save as an .ai, on your computer) Just talk us through exactly what you are doing step by step so we can identify what may be wrong.