I live in Phoenix. That is important to understanding the construction.
The back door is on a slab that abuts to a sidewalk. The sidewalk is not sloped properly. This water hits every other day from the sprinklers. There is no head made that doesn't get a little water on the sidewalk and keeps the grass green.

What are the options for fixing this issue? Is the best bet to remove the sidewalk or is there another solution? I don't want the door rotting out. There is gutter above the whole area and this is the only real problem area. Thanks

And that's not your only problum you have not detected yet. That water water is getting in under that door and rotting out your subflooring.
As you know know that slab should have been pored higher. Your only choise now is a french drain system and getting rid of that concrete around the home.

I bet the house is on a slab too so at least he's safe from subfloor rot.

How about a little landscape change? Get rid of some of the grass in front of the sidewalk near the door and replace it with something like a decorative gravel bed - anything that doesn't need watering. Then reposition the sprinklers so that they no longer spray in front of the door.

The floor is a slab as well and virtually all houses in Phoenix are built this way. This is not unusual. I have suggested the gravel idea to Hubby, who doesn't like it, as he feels it will make the grill area too hot to cook.

This is a newish addition, so I want to avoid rot now.

Do you think the slab could be cut to insert some kind of drain? We are not talking a lot of water at one time.

Build a roof over that area, use light colored stone, anything to stop this from happening.
It will start to show up inside the walls as rotted bottom plate, baseboard, casing, door jams, studs, insulation, water stained carpet, and sheetrock damage.
And if you did install a drain where would you run it to so it does not fill up?

A roof would do no good. It is coming from the sprinklers. We are having a concrete guy come look at it and will probably tear out the sidewalk area and slope it properly.

In a good year, we get 7" of rain. There are gutters and a partial roof over the top. So I think we are fully covered there.

Yes, I live in a very different world from most of the country. Water is not typically an issue, but this sidewalk sure is.
Thanks

you can have him grind the conc slabs so the lawn side is lower than the door side allowing the water to ' run downhill ',,, sealing the threshold properly would also be a boon.

If you have a down spout near the area it is usually hooked to a drain, get some drain pipe and hook it to the down spout drain and put a catch basin in at the lowest spot and let it drain that should take the water away.