I had a stack of my sovereign and 3 champions that I was using to travel around fighting baddies.  At one point, they leveled up and I assigned each champion's point to move (from 3.0 to 3.2).

Next time they leveled up, (after fighting a rather big monster), each champion's move stat was back at 3.0, and I had 2 points to allocate for each.  I assumed that somehow the the game didn't remember the first point allocation, but had left me the point to reallocate.  So I put both points in move for each (from 3.0 to 3.4).

At their next level up, I found that all 3 champions still had 3.0 move, and that time, there was just the single point to spend.  I realized that at the previous level up, they had gone up 2 levels, which was why they had 2 points; not because it somehow kept the point placed into Move.

After that, I put the level-up points elsewhere, and it seems to "remember" them.