How can I secure a post to a conversion ball for a shower faucet?
I am sure that this can be fixed with a thread locker material. There are products available that can be placed onto threads before assembly and then will cure into a very tight joint to keep the threaded fasteners from coming loose. 

You can get this at almost any auto parts store. Ask them for "loctite" thread locker. 



Before trying to use it clean out the threads in both the ball and on the stem piece. Since you already attempted to use epoxy on these parts it may require extra diligence to clean out the thread grooves. Wash the parts in something like rubbing alcohol and then let dry well before applying the thread locker and reassembling. 

Let the locker fully cure before attempting to put torque on the stem and ball assembly.

(Note that I have no affiliation with the LOCTITE brand other than a user).