The number of recent files remembered can be configured at Advanced - Configuration - Toolbars / Menus - Miscellaneous.
The recent files list is updated whenever a file is opened or saved. It looks like you think the recent files list remembers the last X files closed, but that's not true.
So if you use a value of 4 for the recent files list, have already 2 files opened in UE and open by drag and drop 4 more files, the recent files list contains the 4 new files opened. If now a file is modified and saved, this file is added to the list at top or if already within the list, it moves the file to top of the list. If you close this modified file now, so that just 5 unmodified files remain, exiting UltraEdit does not result in updating the list with the last 4 files closed on exit. Whenever UltraEdit is exited with no file modified and not yet saved, the recent files list does not change on exit. The last files saved during exit should be always in the recent files list.
It might be a case that the recent files list is not updated on opening a file. There are more than 10 possibilities within UltraEdit to open a file. If one opening method does not result in updating the recent files list, report it to IDM.