I pick a second combat style, I set up my toolbar the way I want it, I arm the correct weapons and armor, then I save the loadout. I do the same for the other combat style, but when I switch back all my saved changes are gone. I try and switch to the other combat style and those changes are gone as well. Every time I set up a combat style and save it, it disappears when I switch. What am I doing wrong???

If you are using the Combat Skills page to switch, that is what is messing it up. Use the activate button in the lower right of the Loadout screen to switch your loadouts.

 

So, click on the loadout you want, look down at the bottom and choose activate. If it is set up properly it will change your equipment, skill bars and outfit all at the same time.