The human body is extremely economical. Proteins and iron that are built as a response to training are stored, die, rebuilt and stored again. The body will not however, rebuild proteins that it does not need. The consequence of this for an athlete is the rapid reversibility of training adaptations when training is stopped.
How fast?
The adaptations that occur the fastest as a result of training also fade away the fastest. For example a week off with the Flu will result in a substantial loss in blood plasma volume with little or no change in mitochondrial enzyme concentration or capillary density (these are the powerhouse of the muscle cells and the vessels used to deliver oxygen to the muscle). Once over the illness it will only take a couple of training sessions to bring levels back to normal.
3 months off training is a different matter. Research has demonstrated that most of the adaptive foundation gained over the previous 1 years training will be lost. If you are reasonably fit before this then it may only take 6 months to put those foundations back in place. Generally, the fitter you are prior to detraining the quicker the adaptations will be replaced once training is resumed.