Yes, you should care about your people, especially when they give in too fast!
I had one situation today that was really amazing: one of my people said they won't pursue an opportunity, although the most fervant demandeur for it!
What would you do in this situation?? As you are in the fast forward area, where everything has to happen yesterday, today does not exist, and we are always building our future... the most logical reaction would have been: fine, let's see who else would be interested.
But I did one surprising thing: I've asked: WHY do you want to not give it try? And we had a chat about it, and then a face-to-face discussion, where I've listened to the other, trying to understand what was going on beyond the "I don't want it anymore", and asking a lot of questions.
At some point of the discussion, and not even too far into it, the other asked me: why do you even bother with me? I'm a bad person, and I've just changed my mind after it took me an eternity to decide on it... so... WHY BOTHER with me?
That was the most surprising question for me - and I still don't know why would the other ask it. It's so unusual in our world to try to go beyond the words, into other's feelings, into other's justifications and judgements and ideas, understanding and then helping the other, without necessarily having a hidden agenda?
What would you have done in my situation? Would you have asked the other about the motivation, or would have moved further on, relieved that no action is required from you?