Why do athletes see a dip in performance in their thirties?
The decline in athletic performance is a result of senescence; the question then becomes "why do we senescence?"

A number of questions on this site have addressed this. These include Why does evolution not make our life longer?, Why do we age?, and any number of others that one can pull up with a search for senescence. It is key to distinguish between proximate (how, physiologically ) and ultimate (why, evolutionarily) explanations. It's not entirely clear to me from your question which of the two you are asking.