If you take damage and land on CR, can you elect to take knockback?

Or do you have a have CR showing when you take the damage (and what happens if you lose CR after taking the damage)?

No.

You have to have CR prior to taking damage in order to take knockback.

If you lose CR after taking damage (you will have already decided whether to take knockback or not), and you are dealt knockback damage...you will not be able to use CR to reduce it.

Example:

Figure has CR and is dealt 2 damage. It decides to take knockback. It clicks twice and loses CR. It hits a wall. It will take an additional click of damage.