When I first aquired the Skeleton Key in the Thieves Guild quest and picked a few locks I was glad to find you can raise your skill much faster opening difficult locks. But when I had returned the key I was surprised it is gone and it was too late so I added it with console command 0003a070. Now when I pick locks the Skeleton Key breaks just like any other lockpick and I quickly run out of lockpicks (I had something like 60-odd and noticed the number on the bottom right of the screen showing number of lockpicks available decreasing after each unsuccessful pick). But I'm quite sure that earlier the Skeleton Key did not break despite however many attempts it took to open a Master or Adept lock. So are there two versions of it or is the unbreakeability of the Skeleton Key disabled after you return it or am I wrong somewhere?

Because you lack the rest of what made the skeleton key special. Consoling an item in is not necessarily the same as what happens when a quest gives you the same item.

I see. So to use the Skeleton Key in its full potential you must be only at that certain point in the Thieves Guild questline, after aquiring it and before giving it away? No other way after that, neither adding it via console?