Letting rabbit loose in garden?

We have always let our rabbits loose in the garden - its all safely fenced/secure etc. We also have a shed, which the rabbits can go under - its quite low, and it gave our last rabbit a place to hide, and meant I didn't have to worry about cats chasing, because he could quickly dash under there. However he unfortunately passed away, and we found him under the shed - now not sure as to what to do with the next bunny, as would maybe like to block under the shed, but not sure whether this would leave him open to cats?? There are lots of plants etc and medium sized garden, so it's not all open space. Or shall I supervise him when he's out? Which is fine, but means he can't come out for such long periods of time. Any suggestions? Thank you.

IMO I would either offer him supervised time out or build a large pen for him in the garden where he is having the freedom of the out doors but in a safe environment.

Where does bunny live when not free-roaming ~ in an outside hutch or is he a house bunny?

Loxxy runs around my garden pretty much all day when I'm home, but her hutch is always accessible so she can run in there if spooked/hungry/needs the bathroom etc. She can also go into the conservatory which has a dog flap, or the door is wide open. Her hutch is actually just inside our garage which is set back in our garden (not used for car parking!), and I can see her hutch from the kitchen which is nice. When she's out, I open up the run extension on her hutch, and use it to block off the back of the garage (which stops her from getting to things she's not supposed to chew, although admittedly she can leap a fair height so the fence is not a complete barrier there!)

They really need somewhere they can retreat to for shelter, otherwise its the supervision option I guess . If there isn't one outside already, can you put a small hutch in the garden she can get into?

(Loxy is so cute !) I let Smartie run around outside when I get home and she can go into her hutch and my kitchen/diner opens onto garden so I am close by. Think you need to be comfy with the decision you make. Hope that is of some help!