There are currently no
There are currently no rechargeable aluminium air batteries, but they're working on that. Right now, though, the recharging process leads to both degradation of the metals as well as by-product accumulation of other components on the metal plates. Also, aluminium air batteries lose their charge super quickly when stored in an active state. The means once you put that battery in and start using it, you need to keep using it or you're wasting power. People have been working on ways around this (oil and water flushes to deactivate/activate the battery during stop times and try and limit its power loss), but those very same methods for reducing power loss hamper rechargeability. It will be a while before these become efficient long-term energy storage devices, I think.