I use 1/2 cup shortening and 1/2 cup butter in baking chocolate chips cookies but they always fall flat
Maybe you need to buy a new box of baking soda or baking powder?
Baking soda &amp; baking powder can &amp; do lose 'oomph' over time.

Otherwise try chilling the dough for at least 4 hours before baking.
Chilling the dough usually helps butter/shortening based cookies hold their form a tad bit better.