Same issue here with my eduke32. Enclosed is the log if it helps anybody. I'm currently downloading the newest drivers for my card, and if it makes it work I'll post here again.
EDIT: I downloaded the latest drivers for my graphics card directly from the Nvidia website (GTS 250, which is a phenomenal card, by the way), and that did absolutely nothing to help. Then I tried restarting my computer, which didn't help either. I tried vanilla Duke without eduke32, and it DOES save for me like that. I'm assuming that everyone having this problem is using eduke32. If you can stand it, I'd go for that, but personally I prefer eduke32's greatly improved controls.
After I checked that I tried uninstalling the game and then reinstalling it, and then unzipping the latest eduke32 version into the folder (I've tried both the "current version" and the actual "latest version," which are actually two different things, though neither works). It still does not work. I might try seeing if installing it into the default directory it initially wanted to save in works better (I put my games on the D drive, but the original default was the C drive). I might also try an older version of eduke32 than the current, which might affect it. There does not seem to be any reports of anything like this happening on eduke32's official forums, which is very strange to me, but I might ask there too. Currently trying Grombolar's method.
EDIT 2: Okay, I can CONFIRM that Grombolar's method works. The only problem is that the download for it is like 700 megabytes, but if you can deal with it, then it's a very appropriate fix. I'll link you here: http://hrp.duke4.net/download.php
Personally I used the newer 5.1 release rather than the 4.0 that Grombolar used and it works fine. Just pick the one that's right for you. Extract the files into your core Duke3D directory as you did for eduke32, however DO NOT write over the file duke3d.grp. The duke3d.grp that comes with the high res pack is the SHAREWARE version, which will write over the full version, and you'll have to reinstall the game, which isn't much work, but it's annoying.
wait wait wait.....
so everything in the eduke32 zip goes into the Duke 3D folder? not creating another folder for eduke32 inside the Duke 3D folder? do i need to copy the "samples" folder?
So does this mean that the only way to fix this problem is to use HRP huh? I sure hope those guys at eduke better fix this issue soon.....