How are you changing - are you using the Gear Set list?
If you are, it will drop into your Armoury Chest, not Inventory - unless you have changed the settings to dump it in the inventory instead. Check both for your missing gear.

Or, are you saying that it your character just gets naked when you change? You might want to update the set - and/or make sure you are saving all the sets complete. Go through each one. Kit it. Then Update (with the cycle icon button), or save as a new Gear Set, delete the old one.
Either way, your gear should by default all drop into Armoury Chest