Pepper was not fired by Dodd, but by Doug Weaver, a former assistant of Pepper's at Kansas & UCLA. Weaver, a very unsuccessful (11-78-1) HFC in a couple of stops, was brought in when Dodd retired with Pepper's recommendation. The "real AD" from the late '60s til he retired in '79 was John McKenna. From personal experience seeing McKenna around the GTAA from 1968-1972, I can see McKenna not exactly being a Pepper Rodgers fan.
Weaver fired Pepper in '79 & promptly left to go back to Michigan State.
Also during the late '70s, the "Program Killer" Joe Pettit was President of The Institute.
Pepper's persona was always going to have him in hot water with the Piedmont Driving Club & Capital City Club sets, so it's not too surprising the conservative business-types (even some of the ex-HFCs) that run university AAs would shy away from him in that era.