Could it have anything to do with David Silva not being there any more? They have not been able to replace him.
That could be something as Silva did play on his side of the pitch. But Sterling has always had great movement and got himself in goalscoring position with Liverpool and England. So it's not like he has been solely dependent on Silva. He has great instincts. It's just his game hasn't looked as a sharp the last 18-20 months as it did in the previous 18-24 months. Probably could do with a move to refresh him. Sometimes a player needs a new scenery even when they don't even know it. He has a lot of of miles on him he should try a different league/country.
It could be Arteta he is missing.
The timeline fits Arteta leaves and Sterling hasn't had the same high form since. Arteta did do a lot of work with him and Sterling speaks very highly of him.