Yeah, so it's probably rain water running off the roof hitting the slab, then splashing up and hitting the cladding. The cladding won't really dry well once wet because of where it is.
I'd just replace what's rotten, then put some guttering on the Shed to stop the run off falling directly onto the slab
Edit: just seen the diagram, are the runners directly on the slab. If so that's not good. You could raise them with paving slabs so they don't sit in water?