I think of intuition like a channel on the radio. The signal is 100% when I'm tuned in to 98.7 FM, for example. If I'm dialed in to 98.6, I might still hear something, but not as clearly. If I''m at 98.5 FM, not only is the signal weaker, but I may be hearing some of the broadcast from 98.4. Once I realize that the signal has gotten weaker, I tune back in to 98.7.
I apply the same approach while using games to strengthen my connection with my intuition, and find myself experiencing what you described. What I realized is that, over time, I start to think of answers instead of intuiting them. When I notice that I'm trying to use logic and reason (tuned in to a different station), I take a break, breathe deeply, and then go back to the games. Usually, I start performing better.
Elise talks about the same thing in her intuitive reading training - cleaning the slate. Get back to a neutral state where your intuitive impressions are as clear and undistorted as possible.