The regional answer
Middle Tennessee is humid for most of the year and mild through the winter, which is close to ideal for the algae that greens a wall and streaks a roof. Most houses here want a wash every one to two years. Drier climates stretch further; we do not have one.
What pulls you to the short end
Shade, trees and orientation. A north-facing wall stays damp longest after rain. A wall under a canopy gets the same effect plus everything that drops out of the tree. Homes on shaded or wooded lots often want it annually.
What pushes you to the long end
Open, sunny elevations that dry out quickly after rain, and a house that was properly soft washed last time rather than blasted. Killing the growth rather than removing it is most of what buys the extra year.
The tell that you have waited too long
When the difference shows up at a boundary — the shaded end of a wall against the sunny end, or where a downspout has been running. Once you can see the line, the growth is established rather than settling.
Best time of year
Spring and fall are the comfortable windows in Tennessee, though exterior cleaning runs most of the year here. Spring is popular because it clears what the winter left; fall is popular because it takes the leaf stain off concrete before it sets over winter.