I have found that fast travelling to a new location before activating the unencumbered option has a good chance of letting it work. Also make sure you don't have any items with enchantments which affect your carry weight.
we went over this problem over and over many versions back. we tried to reproduce it here but could not. we showed that the trainer was working on savegames that people sent that said it wasn't working. it isn't that we dont believe you, it's just that we could not reproduce the problem here.
well, people got so agitated and snarky with us that we ended up stopping updating the trainers and dropping this title.
after overwhelmimg messages from memebers who appreciated the trainer as it is, we re-released it.