The fin was shortened to lessen the structural loads (torsion and bending) when flying low (thicker atmosphere). That and using a spoilers-only roll control presented issues:
To reduce aerodynamic loads on the rear fuselage in low-level flight there was a 91-inch reduction in the height of the vertical stabilizer. This stubbier fin had been tested on the first B-52A. In practice, the short fin combined with spoilers-only lateral control induced a tendency to Dutch-roll and low level handling was more sensitive than on earlier B-52s.
— Davies, Peter E., Tony Thornborough, and Tony Cassanova. Boeing B-52 Stratofortress. Crowood, 1998.
Related: Did the "feeler" ailerons of the B-52A-F make air-to-air refueling easier than with the B-52G/H?
The structural reason is also mentioned in an AeroTime article:
The shorter vertical fin was intended to prevent the aircraft crashes caused by the original tall fin failing in turbulent air.
On Wikipedia's B-52 article, there are at least two such accidents:
- On 24 January 1963, a B-52C on a training mission out of Westover Air Force Base, Massachusetts, lost its vertical stabilizer due to buffeting during low-level flight, and crashed on the west side of Elephant Mountain near Greenville, Maine. Of the nine crewmen aboard, two survived the crash.
- On 13 January 1964, the vertical stabilizer broke off a B-52D in winter storm turbulence; it crashed on Savage Mountain in western Maryland. The two nuclear bombs being ferried were found "relatively intact"; three of the crew of five died.
While those accidents were on older models, they took place after the change. That does not mean the structural integrity was not apparent from regular maintenance or from manufacturer data. The list is also not exhaustive, there could very well have been minor failures that did not make that list of "notable accidents".