After all that Skinner did for the dynamic duo, ranging from selling his soul to the Cigarette-Smoking Man to try and save Scully from her cancer to pledging his support for the X-Files unit after Mulder's abduction and Scully's pregnancy, it will probably take something pretty huge for him to lose their trust. Dealings with the Cigarette-Smoking Man are a pretty solid way for folks to alienate Mulder and Scully, as Scully even turned on Monica Reyes in Season 10 when Monica revealed she'd been pressured to help the CSM after Scully left the FBI at the end of Season 9. Incidentally, Monica will be back in Season 11, so maybe we'll get to see her and Skinner together as a pair of former trusted allies whose loyalties are in question.