there are battlefield requirements to upgrade pieces to the 119 level, and they vary based on the equipment family (artifact, relic, empyrean). For artifact,
here is the link that goes over the basics.
If you have completed this already and are having issues, check and see if Monisette is waiting to give you a piece back that you've forgotten about. She won't start reforging a piece, even if the time has passed properly, until you collect the current piece. Just a possible thought.