I don't think there is any 'Code' deflection limit on shoring systems. FHWA has various documents and there is the old NAVFAC design manuals that give recommended guidelines. I am not sure if AASHTO gives hard limits or not. It really depends on why you are digging the hole, what goes in the hole, and what is above the shoring.
If there is a building on shallow spread footings directly above the shoring you want to design for at-rest pressures so you need a stiff structure. If you have a shoring system that will be part of a one sided form you will need to coordinate with the EOR of the building to make sure your shoring deflections will not eat up too much of their wall thickness. If you have a hole with some extra space inside you can live with some sizeable deflections that will some with getting members right up to their design limits. It is up to you to decide if your shoring deformations are acceptable.