I'm thinking you probably have to upgrade the whole weapon, which is a pain because the suppressors are ridiculously weak in this game. It's going to be a long time before I can upgrade my tranq pistol to level 3, and right now the suppressor breaks before I've even fired the 21 measly shots I deploy with.
You can actually find suppressors out in the environment, but I've only ever seen one and I'm not sure if you can actually 'store' a suppressor like you could in MGS3. It seems like they're equipped automatically; I don't know if you can pick a suppressor up, break the one you're using and then equip a new one. Either way you can just call in a Supply Drop to get a new one, though.