A blocked eavestrough does its damage in the two seasons nobody is looking: water spills over the edge, saturates the ground against the foundation, and in winter freezes into the ice dams that push up under the shingles.
Twice a year, and the timing matters
Late autumn, after the last leaves are down, is the important one — that is what prevents the ice damming. A spring pass clears the seed and blossom debris that has built up over winter. On a heavily treed lot both are worth doing.