Great question — answering as the UphillTech team:
Usually when cookie dough falls apart, it is because the flour is not sufficiently hydrated, that is to say, it has not absorbed enough water. There are two factors at play: The ratio of liquid in the recipe (from eggs, milk, water, juice, coffee, or any other source) to flour (by weight) The amount of time that the dough has had to rest and absorb the water. Typically, when you are saying your dough is crumbly, it is going to be a rolling type cookie, like a sugar cookie. These often benefit very much from a resting period of at least four hours in order to fully hydrate the flour. Another common cause is measurement. Flour, especially when measured in a measuring cup, is very easy to...
Full answer by SAJ14SAJ: https://cooking.stackexchange.com/a/37127 (CC BY-SA 4.0).
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