How to paste a logo into all artboards in same place

Do you want it to be at the same distance from right/bottom sides?
If you mean top/left sides, the command works fine becouse Zero for each artboardis TopLeft corner and all the distances start there. But for the opposite side the way is a bit more complex.
I would suggest the follow:
1. Define the offset which is suite to the smallest artboard and put the logo on the firts artb. at this distance from Zero.

2. Cut the logo and use Edit > Paste on All Artboards.

3. (it's the longest part): align each logo to the right (or bottom) of its artboard (make sure that the artboard is active, choose Align to Artboard option).

4. Select all the logos and move them to the needed position using Move tool. 
Actually, this takes about a minute for all.

But if you work with Top/Left sides, the normal way works fine.

Do you have all your artboards set to the same top/bottom alignment..? There should be no reason that this is not possible..?

Can you send a screenshot of how you have your artboards laid out?