Baba lysaga
In the bo1 cube draft event, I blocked one of my opponent's attacking creatures with baba lysaga, night witch, and wanted to activate it to sacrifice it, my dollhouse of horrors, and a land to gain 3 life and make my opponent lose 3 life. They were at 4 life and had Black Market Connections, and unless they could destroy their own black market connections before the next turn, I had the win, but I lost the game because I couldn't tap baba lysaga.
One of the previous games had the same problem. I wanted to tap baba lysaga at the end of my opponent's turn, but the game did not pause during their end step to let me activate it. In that case, I still won the game, so it didn't matter, but it was much closer than it should have been.
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[Deleted User] commented
Did your opponent control a Myrel? She shuts down your activated abilities during your opponent's turn.