Go to My Documents/Illarion/Character Name Here/ and make sure there is a file named "names.tbl" there. Open it in Notepad and make sure you can see a list of names there. If you don't, get in-game and walk up to an NPC for 10 seconds or name someone something then check again. Shut down your PC, start it again and check if it got deleted. Post results here.
Are you literally going in the Illarion folder and noticing there's no "names.tbl" file in your character's folder? Or do you open the names.tbl file and it's empty? Are you using CCleaner?
Out of curiosity, you're not clearing the java cache regularly or something are you? Do you have to redownload the client every time you play? CClear might clear the java cache if you ask it to (default is yes I believe) - but I wouldn't think that deletes the folder and the items in it though.
Another idea: make sure your names weren't saved by notepad as names.tbl.txt (sometimes the txt may not be seen). Look in folders/tools/file types and see what is listed to open a tbl file making sure any office program didn't change it to that as default.
Did you maybe set the path where the client is supposed to store the informations to a location where the client is not ALLOWED to store the informations? Windows Vista/7 tends to deny access to a wide range of folders for java application. It works best in case the folder for the files is inside "My Documents".
@Karl - There is a names.tbl file, but when I look in there are no names in it (After they are deleted. There are still names from people who re #I yesterday though.)
@Hadrian - I'm not sure if my computer has CClear on it, but I'm not having to redownload the game every time I want to play.
@Achae - It is a .tbl file
@Nitters - I am honestly not sure if I set the folder to be updated to the "my documents" folder. If I did not, how may I check this to make sure? Or should I just uninstall the game and try it another way.
Also, an update. The last time the compy forgot everyone, I did not shut down. I just logged off one night and the next morning everyone looked like Short Elfess and Tall Elf.