mhh, likely some file on NAND got corrupted... I'm not sure what it would be, you may be able to fix it by restoring an old NAND backup or making a new one, checking for any seemingly broken files, testing in no$gba, and if fixed restoring that.
Whatever you do, assuming you have it, do not uninstall Unlaunch. I had that happen on one DSi and it bricked on uninstalling Unlaunch. I happened to have a NAND backup from shortly before uninstalling and the brick was 100% consistent in no$gba so it's very likely your console would brick without Unlaunch atm.
If you don't have a good NAND backup I can try testing on my backup to see if I can find the cause of the positions not saving, I haven't really messed with it much. It's possible it's caused by the first few hundred bytes of the DSi Menu's title.tmd getting 0'd out, that's what caused mine to brick. Not sure how it happened, but by uninstalling Unlaunch it exposed an issue already present but previously kept safe by having Unlaunch.