You failed to mention if this hub is an existing unit on a bike which used to work and all of a sudden failed, or if it's a new installation.
Providing the hub itself does not have an issue, the most common cause of an NX3 not reaching 3rd gear is the push rod is not being pushed in far enough, for whatever reason.
If it's a new installation, remove the bellcrank from the axle and verify that the pushrod can be manually pushed all the way in without jamming up. It should slide in and out, freely, with the exception of feeling the internal return spring tension.
If that all seems good, measure how much axle length is protruding past the outside face of the axle nut, on the bellcrank side. It should be between 8 and 12.5 mm. If it's less than 8 mm, this certainly could cause loss of third gear. See pic below:
I've seen where people add a spacer between the axle locknut and dropout, causing the axle protrusion to be too short.
If that appears good, open the bellcrank and verify the lever moves freely without hanging up, and verify the shifter or cable is not jamming up before reaching the 3rd gear "click".
There are 3 different axle lengths used on the coaster brake NX3's. The most common has an axle width of 168 mm, and requires an 81.85 mm pushrod. If the axle width is 175, or 178 mm, the pushrod needs to be 86.85 mm. Make sure you're using the properly sized pushrod for the axle width of your hub.
The above specs are for coaster brake versions of the hub, and the specs are a bit different for the roller brake, and disk brake versions.
If you're positive all of the above is correct...... suspect your hub's internals.
