Staying active only requires that you show an ability to not be defenseless. Also, the current standard for stoppages are horrible. 90% of the time, fights are stopped too soon and you witnessed a rare case of decent reffing.
If Brock went limp while on his back even for a second, then yes, stop the fight, or if his eyes rolled to the back of his head, then yes, or if he isn't reacting by pushing off with his legs, flailing his arms in defense "attempts," then yes.
I think there were multiple instances where Carwin could have finished it if he landed more punches in a row, one after another, but they were too hit & miss, which is great for damage in general, but hurting someone in of itself doesn't justify a TKO.
I've seen refs stop fights in much less dire circumstances then what Brock was in and I've seen refs let fights go a bit too long, like Carwin/Mir or even Brock/Mir II. Each situation isn't measured to a science, the spectrum of stoppages are all over the place, what seems to make it right or wrong is which side of the fighter you're on. It happens.