This is long lasting I have noticed, where either the turret (specifically Spitfire for me) or ammo box gets stuck in its cooldown state, and you cannot use it. You have to restart the whole game to fix it. I don't play Engineer but when I do this happens quite often and I don't understand how it doesn't get more complaints.... Unless there is somebody tampering with the game values, like last time with the flying turret. I have also heard speculations from others of, like as if people's accounts got infiltrated somehow, to mess with them... So, that is a whole other level from the flying turret thing.
It also affects medic's shield regen field and infil's motion spotter. It gets stuck in cooldown state when you're get killed during animation of placing it
IIRC i can normally fix that bug by changing my loadout, putting some other DEPLOYABLE item type in that same slot (or number), and then deploying that. ie: if you can't put down a spitfire turret, then just change the spitfire turret to a deployable hardlight barrier, then deploy that somewhere. Now change back to having a spitfire turret & it should be fixed. You tend to need something of the same item type, ie: if a deployable item is bugged you'll need another deployable item. If it's your ammo pack that's bugged, then you might need another similar throwable item like the sniper's anti-infantry mine. You may even need for it to be in the same slot number (so you may need to remove or add some items, or change to a different class entirely, just so that the item is on the same weapon-selection number)