Yoto Adventure Jackets and travel cases
The jacket protects against knocks and grubby hands. The case protects against the car. Neither protects against a hard floor, and they are specific to a generation, so check yours first.

It is going to get dropped
Adventure Jacket
Yoto·Researched, not tested
Silicone skin that fits over the player and leaves every button, port and the nightlight reachable. On the full-size player there is a lip at the front that lifts the display off the surface in nightlight mode, which is a thoughtful detail. The Mini version comes with a wrist cord.
The catch: It is protection against knocks and grubby hands, not against a hard fall onto tile. Third-party silicone skins on Amazon do much the same for less if the colour does not matter to you. This one fits the 3rd Gen player only; the 4th Gen has its own jackets.
See it on Yoto
It needs to survive the car
Yoto Mini Travel Case
Yoto·Researched, not tested
Hard shell taking the Mini, cable, headphones and around thirty cards, with a shoulder strap and a port so it plays while shut. The item parents most often say stopped them losing things.
The catch: Priced as an official accessory, and third-party hard portfolio cases do much the same for noticeably less. Worth comparing before buying.
See it on Yoto
The Mini is going to be carried by a small person
Adventure Jacket Mini
Yoto·Researched, not tested
Silicone carry-case that fits snugly over the Mini and protects it from small bumps. It has a wrist lanyard, so a child can carry the Mini without gripping it, and it comes in a choice of colours.
The catch: Protection from small bumps, which is how Yoto describes it, and not from a hard fall. Jackets are specific to a generation: the 4th Gen Mini has its own with a new lanyard, so check which Mini you have before ordering.
See it on Yoto