Well, this was the most interesting thing which happened yesterday.
Kerillian was downed/died and was revived/rescued (I do not remember which one). Thereafter, she stopped responding. Our host slowly nudged her thru the Skittergate. Once over the threshold, she came back to life.
On the return, she stopped responding after passing thru the Skittergate. Somehow, she came back to life again after some time and we continued.