CM9 skips to the next song, even on short presses I have a Motorola Defy (MB525), running Android ICS (4.0.4), CyanogenMod 9-20121116-NIGHTLY-jordan, and the option to skip to the next / previous songs on a long press of the volume buttons is active.

It is intended to skip to the next song only after a long press, but even after (very) quick presses, it skips to the next song, and my only option is to disable it completely.

In short: it seems to be considering any press on the volume key as a long press, regardless of the duration.

Is there any sort of fix?
The only recommendation I can give is to upgrade your firmware. You could try a newer version of CM9, as then you don't have to wipe data. If you want a fairly stable newer version, 4.1 works really well, and 4.3 somewhat. Go to quarx2k.ru and select the 2nd-boot folder for them.