Try to think of a single action you could take that would improve your self esteem if you and everyone else were immortal. Try to couch the reason for valuing this action in Objectivist terms. I can't do it, since everything in Objectivist morality and ethics boils down to making life-affirming choices. We all have different issues that on occasion encourage us to engage in repression, rationalization, denial or avoidance of some form or another. For example, maybe a person is a touch more sensitive about something in their appearance than they should be. When someone, or something, reflects this to the person - at that moment the person is presented with a choice point. They can engage in some form of avoidance or they can experience a moment of pain which comes with more deeply accepting this aspect of their appearance. If they engage in self-acceptance, after the moment of pain, there comes an increase in self-esteem.
Self-esteem is an automatic, and unavoidable effect of certain conscious processes. When we engage in various forms of neurotic defensiveness (repression, denial, etc.) there will be an automatic, and unavoidable decrease in our level of self-esteem. When we use our consciousness in those ways that are healthy (self-acceptance, self-responsibility, living consciously, acting with integrity, being assertive, etc.) our self-esteem will automatically increase. This constant up and down is additive and over the course of time determines the extent to which we will have this background feeling of being competent to handle what the world presents us with and feeling that happiness and being lovable is appropriate to us.
When this background experience - self-esteem - runs high enough it is very empowering - like a high octane fuel. When the feeling is very low it becomes a strong motivation to engage in neurotic defensiveness. It is the reward for using your consciousness in the proper fashion, or the punishment for using it in the wrong way.
I think this makes it clear that self-esteem is a by-product of the way a person uses their consciousness and that I don't think it would be directly effected by becoming immortal. In fact, without mortality, self-esteem would be more important as a goal, and for the reward it can constitute.
I wouldn't put self-esteem into the category of Objectivist philosophy, but rather into psychology, which rests upon the philosophy of psychology which in turn rests upon philosophy.
Talking about the Matrix, you said:
There would have to be some struggle, some sense of accomplishment. You can't win in life if there is no possibility of losing. ... We need a certain amount of risk and struggle to remain human. I agree with this. But I don't think it will ever be possible to eliminate risk. We just change the kinds of things at risk. To make a choice is to risk being wrong, and we choose everything - including the person we are.
Just a note: I'm not a "former psychiatric professional" - that is a license only granted to people who have a medical degree. My degree was a Master's level degree in clinical psychology.