Just my own humble opinion, but I would argue the opposite: mathematics is so technical and - depending on what field one goes into - the amount of time that it takes to develop mastery sufficient to create new mathematics can be up to several years. In my experience the theorems that are the most deep are the ones that take more than technical expertise. They require insight into the heart of the mathematics and a view of the overall structure of *many* results that fall under the umbrella of the theory. This kind of thinking is more than just mastery - it's keen intuition, near encyclopedic knowledge of the current field, and technical fluency rolled into one. Certainly, I personally know of people making new and relevant mathematics well into retirement....

But one can also come up with plenty of counter examples of this hypothesis. Eugene Wigner (b. 1902) proved his famous "Wigner's Surmise" in 1952. Minoru Tomita's (b. 1924) manuscript on Modular theory (1967) was reinterpreted by Masamichi Takesaki (b. 1933) and is of fundamental importance to the theory of type III factors. Kyoshi Ito (b. 1915) published his work on stochastic integration in 1944 which forms the foundation of the entire theory of stochastic SDE. Roger Penrose is in his early 90's and is still working. Florence Nightingale (1820) used novel data visualization techniques in the late 1850's (from what I can tell; the Wikipedia account of her work in statistics is vague). Julia Robinson (1919) and collaborators showed that no algorithm exists that can tell whether a Diophantine equation has any solutions in integers in 1970. ... The list goes on.