Col. Wilma Deering is a terrible flight combat commander. She managed to get four of her troops killed in about 30 seconds in the first part of the first episode by relying on the "combat computer."
Buck Rogers also contributed to their deaths by yelling archaic phrases through the radio system, like, "Bogey at 12' O Clock!" A confused fighter pilot, trying to figure out what a clock had to do with anything was vaporized seconds later.
It seems probably that Wilma Deering only has her high-ranking Defense Dept. position because her father is a respected statesman.
Also, living in Chicago are zombie-mutants, almost straight out of The Omega Man with Charlton Heston. Buck Rogers is totally oblivious to the danger he's in, let alone to exposing Dr. Theopolis of the Computer Council to almost certain doom. It seems odd they'd have no way at all of calling for help, but there you have it.