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OK guys it would seem that the problem is that the server is just not updating our progress.
Progress seems to still be there, it's just not showing up in our party menu.
Here's a GIF to demonstrate.
Basically, when I logged off last night my Leafeon was level 14. Today, I woke up and leveled it up to level 30. I taught it Sword's Dance(Level 29) as well as Giga Drain(Level 25).
When I logged off and logged back on, it appeared that my Leafeon was back at level 14 like last night.
However, in battle, if I use the moves that I overwrote to make room for Giga Drain and Sword's Dance, it still uses the moves, indicating that they're still there.
You can also see that when you battle your Pokemon's HP loss and Levels don't update.
It's possible that it's all still there, just not showing properly.
This doesn't mean that you should take the chance (unless you really want to), but it does mean that progress may still be there and not gone for good.