"has slipped down" is correct and usable in written English.
You can use it to refer to a person or object that has moved downward. For example: "The child has slipped down the slide."
It has slipped down a bit – I read that someone was murdered there.
After that heat, Payne has slipped down to tenth but could still make the semis.
Following her high profile in 2012 as presenter of the Paralympics, Clare Balding has slipped down from last year's number four position.
The civil rights drama took the top spot in its first two weekends and has slipped down a notch, but no matter – The Butler is well on its way to taking in more than $100m.
In Pripyat, the plant workers' former bedroom community, a little over a mile from the plant, where 50,000 people were given a few hours to evacuate, wallpaper has slipped down under its own weight and paint has peeled away from apartment walls in fat curls.
The four-time world champion has slipped down to sixth in the rankings.
At the end of last year he had slipped down to 40th in the world rankings.
With Europe and Russia having slipped down on the Pentagon's priority list, a new Cuban missile crisis appears improbable.
Jobless claims have slipped down to 264,000 with the four-week average of 271,750 – the lowest in 15 years.
Bank bosses have slipped down the pay league since the financial crisis devastated their industry and reputation.
He was dead – stiff and cold … I had to remove his identification tags, and they had slipped down between his collar bones and the flesh of his chest.
