You have to choose an airport above alternate planning minima ("wx better than good enough") to nominate it as a destination alternate.
Once airborne, that destination alternate should be above "good enough minima" or published minima, for you to count on it. Therefore, once airborne you can keept it as the alternate as long as you can land on it according to the plate minima.
But: if you make an inflight replanning to another airport any alternate for taht airport must meet planning minima, bacause you are in planning stage again.