Is your My Documents folder in the stock location? (you haven't moved it??)

Look in your oblivion.ini, and find the setting:

SLocalSavePath=

the value should be Saves\

Yes, both of those conditions are met (I think I read that on the nexus forums as well so I had checked it out and neglected to mention I had done so on this forum)

That is just really bizarre........ I am really curious where the process is breaking down at, but, I don't know of any tools that would give answers that I would understand.

Try playing the game in windowed mode, and have your saves folder open in another window. try and repeatedly save the game, either via menu, quick key, or console, and refresh the saves window after each attempt. (just make it the active window, and poke the F5 key.)

See if ANY of them want to work that way.....

Ayal, I still think your problem is due to the game itself being installed C:\Users\"Your Name"\ Favorites and the fact that saves go into C:\Users\"Your Name"\Documents.
EDIT I tried to duplicate your problem by installing Oblivion into Favorites, the saves worked,follow HeyYou's advice, I am curious what the issue is myself.

That's the default location where Oblivion decided to create the saves, so...yah. Worked for 100 and some saves before, so I'm not sure. Anyways, like I said I have done a new install directly onto the C:\ and saves are now in C:\Documents\My Games\Oblivion\Saves, and the issue pertains.

I'll try that next HeyYou.

Something else to try..... Rename one of your saves so the numeric index is 1. See if it will let you save then....... Move all the rest out of the folder.