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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 slabEdit: 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?
The fence side is, but unsure of the others. Thinking a preventative would be to put two bearers down.
Hopefully this pic and diagram show the situation. I need to find a time in the morning when my kid isn't around to check the water flow. Previously there was a lot of crap down there which wouldn't have helped with avaporation.