You could try concrete crack filler, but concrete is porous. I would recommend a concrete curb that would help to push the water off to the edges. Water will take the path of least resistance. You just want that to not be into your shed.
Home Improvement
Home Improvement
Without a real sill and a slope on the outside your going to have water intrusion. Add a gutter/diverter above the door on the roof. Remove all the sealer you can. Use waterproof concrete sealer/paint on the slab. Fill every gap you can with silicone. Shave down the slab with an angle grinder to add some kind of slope.
If the concrete applier 'forgot' to add a slope to the outside see if they will help with the remedy.
Thank you for all your very useful suggestions!
Do you think cutting a draining channel into the slab just outside the door (instead of sloping the entire slab) could also work?
Maybe? When it rains you need to move lots of water fast. It'd need to be a serious channel
It seems like the water is probably getting higher than the sealant. At that point, it's almost certainly a manufacturing thing with the door that you can't easily fix. A sill would be the best bet imo.
Do you have eave troughs there by chance?
No, the gutters and downpipe are on the other side. There is a bit of flashing above the door though.
Do you think water could be leaking from there?