- Is it affecting only specific ninjas?

No
- Is it affecting all special skills?

Yes
- When are you experiencing such problems?

Most of the time, it goes like this. You wait for the opponent to use up all his ninja's turn and then use a mystery to disable his last ninja(positioned in the 3rd row most of the time) so it carries out onto the next turn but what happens is that the skill don't push through and instead used immediately in round 2.

- Is it happening during specific in-game timed event or is it random?

It happens a lot in arena, swb and matsuri. It never happened to me in space time but then again I haven't fought a lot of battle there.