I'm not sure what they did to counter the takedowns - as I said, I didn't stop at the time to explore it, but I wish I had. As I recall, a couple of them were counters to variations of an arm drag, and the others were to single-leg takedowns and hip throws. In each of the cases I remember, as soon as they stymied the takedown and I started moving my weight out of it (to close the opening it had presented), I immediately felt that "void" that tells me there's an easy aiki opportunity. I shifted their weight into it and they dropped without effort. I can only remember this occurring a handful of times.
It might have been simply an overcommitment to the counter by shifting their weight against it (which would easily produce the effect), or it might be that whatever counter they used would put their weight in the right spot every time. I wish I knew, both as a possible opening and as something to avoid, myself.