Overexertion depletes the regular energy stores and further energy relies on the break down of energy stores (eg fats), which need to be delivered to the cell first and then into the mitochondria.
As to what damage, it depends on what is happening to the muscles, what disease you have etc.
The half life of mitochondria is 2-4 days, depending on their location. Simply put, direct damage to mitochondria does not stay for very long. If there is damage, then there must be an ongoing process either cellular (eg cancer, or genetic diseases), or is a consequence of something interfering with extracellular signalling (that causes downstream dysfunction in the cell) that causes this damage. Deconditioning and other diseases can also lead to lower mitochondrial numbers in cells.
http://www.jbc.org/content/256/16/8652.full.pdf
There is no direct evidence for dysfunction within the mitochondria in ME/CFS patients, there is however some evidence for dysfunction of fatty acid metabolism (which seems reasonable given the time periods of the PEM), perhaps something is limiting the proceeding metabolic process of fatty acids getting into the cell, or the mitochondria in the right form to be metabolised.