Perhaps Sullivan was just at odds philosophically with Armstrong, hence the initial switch from doing GM things to scouting, and then on Sullivan's second chance he didn't adapt to what Armstrong wanted, hence getting terminated. I really doubt this is much more than the brain trust all needing to be on the same page, and that page being distinctly different from what it was under Chayka.
His initial demotion of duties might also have something to do with how he handled the interim position. I know he was getting intel on trade valuations, but if Armstrong really didn't want to trade OEL, OEL didn't really want to be traded, and ownership didn't want to, but deferred to management on what to do, and yet Sullivan still went about shopping him, then I could see Armstrong being pissed that Sullivan credited that headache for him to fix on day one. I could see Armstrong giving him the benefit of the doubt even though he hated how he'd handled that, but after reassigning him within the team and still not being impressed with him, he's finally just given the axe.