What sort of things affects the chances of recovering files?
No. Once it's been securely deleted, it's gone forever.
Recuva cannot delete files that are resident in the Master File Table (MFT), or files of zero size. Resident files are very small files (typically a few hundred bytes) which are so small that Windows stores them directly in the MFT. Zero byte files have no size and therefore have nothing to delete.
This can happen when the file you deleted has already been overwritten with another file. Check the Preview pane to see if the file still contains the original content. The Header pane displays the first 128 bytes of the file, but it may not change if the first cluster of the file you deleted has already been overwritten with another file.
If you have used Recuva (or any other similar application) to erase files, the files may still be marked as being recoverable, but they are not. The file marker may still exist, but the contents of the file will be gibberish.