Why does "for that" change the meaning if combined with "up," but not with "down"?
The phrase "for that" does not really change the meaning, but up is just not used alone in that sense.
up is more easily understood in the denotional sense when it appears alone, because we are up most of the time. That's why down as a shortform of down for that is allowable, if I can already see that you are not physically down.