Acceleration is the rate of change of velocity with respect to time, and velocity is the rate of change of height with respect to time (if we are just considering vertical motion).
If you define height as increasing as you go up (which is the usual convention) then in ballistic motion height increases to a maximum value and then decreases. So velocity starts out positive, and decreases both on the way up and on the way down - remember that a velocity of $-10$ m/s is less than a velocity 0f $-5$ m/s. So the acceleration due to gravity is negative throughout the motion.
On the other hand, if you define height as decreasing as you go up then in ballistic motion height decreases to a minimum value and then increases. So velocity starts out negative, and increases both on the way up and on the way down. So acceleration is positive.
In other words, once you choose a direction for increasing height, the sign of the acceleration due to gravity is then fixed and stays the same throughout any ballistic motion.