It turns out that wget defaults to 5 levels of depth, even when downloading physical files from ftp (rather than following symlinks). I changed it so it so that it uses 10 levels instead with -l10 and it was fine. The number of levels make sense when you see the default output structure of servername/dri1/dir2/dir3/dir4 even though your files might appear to be level 4.
I'm not sure if rsync is easier to use for this purpose but the wget command is easy enough:
wget -r -N -l10 ftp://username:password@servername/dir
Where -r is recursion, -N only gets items that have been modified and -l10 increases the number of levels to 10 (That is 'L' 10, not 110!)