I think there is 1 big issues for Skinner and 2 small ones.
The big one: Neither McDavid or Drai seem to enjoy playing with a winger that likes to fade into the background and find soft spots in coverage (the Ebs/Skinner, type), or someone who likes to control the puck and play the game their way (see the friction at times between Kand and Drai).
For the last half-decade the MOs of the wingers that work well with McDrai are either a) guys that are willing to hound the puck up and down the ice, and quickly get it back to the centre. (RNH, Podz, Hyman, Foegele, McLeod, Pulju, Yams; Or b) Have the size and willingness to go to the net and occupy one or more defenders (Hyman, Kane, Maroon, Kassian, Chiasson. and Neal.
Considering this team has several guys who fit those templates, it's not hard to see how Skinner hasn't gotten a chance. For a winger who's only useful when they're spoonfed offensive usage, Jeff is potentially 6th or 7th in terms guys I'm tossing out there when I need a goal.
McDavid
Drai
Hyman
RNH
Arvidsson
Skinner/Henrique?
2) Thanks to his skating, Kapanen has come in and more or less stolen Skinner's potential spot as the offensive winger who bounces up and down the lineup as needed.
3) Kane will be back by the playoffs, and brings far more to the table.