Beethoven chose A-flat major as the key of the slow movement for most of his C minor works. This was also followed by Antonín Dvořák in his only C minor symphony and Anton Bruckner in his first two C minor symphonies.
Since A-flat major was not often chosen as the main key for orchestral music of the 18th century, passages or movements in the key often kept the timpani tuned the same way as they were in the movement before it. For example, Beethoven's Symphony No. 5 in C minor has the timpani set to C and G for the first movement. With hand-tuned timpani, there is no time to retune the timpani to A flat and E flat for the slow second movement in A flat. In Bruckner's Symphony No. 1 in C minor, however, the timpani are retuned between the first movement in C minor and the following in A-flat major.
↑Charles-Marie Widor, Manual of Practical Instrumentation translated by Edward Suddard, Revised Edition. London: Joseph Williams, Ltd. (1946) Reprinted Mineola, New York: Dover (2005): 11. "No key suits it [the flute] better than D♭ [major]. ... A♭ [major] is likewise an excellent key."