The solution is quite simple. Use (always the same) named files for text to keep on UltraEdit exit instead of new, unsaved files.
See forum topic Automatic save of new files on exit and reload on next start with automatic delete on saving/closing new file
linking also to forum topic Save all new, unnamed files with automatically generated file names
But honestly I don't understand why people copy or write data to keep into new, unsaved files instead of (always the same) named files and complain that UltraEdit does not keep them automatically on exit and instead asks the user if the new, unsaved file should be closed or saved.
It would be also possible to create a macro which is stored in a macro file being automatically loaded on startup which has Ctrl+N as hotkey and which creates a new file and automatically saves the new file with a file name. A script could be also used to implement a create new, named file. Then it would be possible to use always save all without prompting for file name. But again I do not really understand why not using (always the same) named files for text to keep on exit of UltraEdit.