Apparently there is no consensus on naming this phenomenon in the Anglo-Saxon culture. The worst name is definitely "Eternal Rook Draw" as it lost the action involved and the implied state of "Eternal Draw" is weird as well. But there is nothing wrong with "Rampant Rook". I hope the future belongs to "Rookamok" though.
Forcing a draw when you're losing
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As @BobbyGotFischered mentioned above, it depends on the position but forcing a game to be a draw by 3-move repetition is more likely than forcing a draw by 50-move rule. If you can really play 50 moves of constant checks, the position would likely have been repeated or your opponent would have found a way to block a check.
A few years with our AMAZING LINT chocolate and coffee making facilities and services to worry about it is a few days ago 😞
... Then, I found out analysis said that there was a brilliant move for black that was the start of the draw. There was no solution to get rid of draw if black wouldn't do a blunder. Also if I wanted to capture the rook, it would be a stalemate ....
This is known as a "crazy rook" though I prefer the name "rookamok" which has a great rhythm and was proposed by a user on chess.com. It is not uncommon - even in human games. Some compositions demonstrate long cray rook runs (dozens of moves) and finding the right checks or escapes may be complicated. Learning about crazy rooks is part of the education of every chessplayer and every puzzle solver.
By crazy rook, do you mean the Rampant Rook or Eternal Rook Draw?
I had the following as Black against a master over the board in March:
Just 1...Rg3+ and continue to check the king across the third rank. It is perpetual check or stalemate, depending on what White does.
EDIT: There was also a white pawn on f6, but that doesn't matter!
I should also add it was a little more concealed at first. WK was on g3, BR on c7. I did 1...Rc3+ and now Kf4 I check along the b-file, he cannot hide. Kh4 Rxh3 Kxh3 is a draw, and K to anywhere on the 2nd is the eternal rook draw shown above.