I usually work with a set review point instead of a fixed number of months for everything. For on page changes I expect some movement sooner, as Starblazer mentioned, while links and new pages need longer to show anything useful.
What helps me most is writing down the starting point before I change anything. I note the queries bringing impressions, the pages getting clicks, and whether the page is actually indexed for the terms I want. Then I check the same points again after a few weeks. If impressions are spreading to more relevant queries, even without clicks yet, I leave the main approach alone and fix smaller things like the title or the opening section.
If nothing is moving at all after two or three months, no new impressions, no change in position for the main terms, and the page is indexed correctly, that is when I look again at intent and competition, like several people here suggested. Changing one part at a time makes it easier to tell what helped, which is the point littlepuzzle made and one I agree with.