How long can a tree survive without water?
It depends on so many factors that the question doesn't really have an answer. Of course it depends on the specie of tree, but also on the development of root system, the age and condition of the tree, and other factors (such as sun and temperature) in the environment. A young seedling might survive only a week without soil moisture, while a mature tree adapted to desert conditions might survive a couple of years. Note that most desert trees have roots than go very deep into the ground, so although there may be no rain for a long time, the tree still has access to water from the deep places.