You do not say what field of mathematics you are working in, and perhaps there are signs of separation there. Overall however, lively interaction between mathematics and physics is alive and well. John Baez has a blog This Week's Finds in Mathematical Physics, that is full of contemporary examples of it, so does Terence Tao. Nature, a leading journal in empirical sciences, just published a mathematical paper Undecidebility of the Spectral Gap related to one of the millenium problems, which in turn came from quantum field theory.
One example is the Fields medal awarded to Witten for his insights into the mathematical structure of gauge theories and low-dimensional topology that were obtained by combining advanced mathematics with heuristic physical reasoning. Converse example is the mirror symmetry conjecture in algebraic geometry that came from string theory physics and led to foundational work by some of our leading mathematical lights like Givental, Kontsevich, Fukaya, etc., which is ongoing. The Gromov-Witten theory, a major mathematical advance in algebraic and symplectic geometry, grew out of this circle of ideas. Okounkov received Fields medal in 2006 for his mathematical work in it partially done in collaboration with leading physicists like Vafa. More recently, large N duality and holography conjectures received the same treatment.
This is not restricted to frontier quantum physics. General relativity continues to present deep and intricate problems in (pseudo-)Riemannian geometry, and cosmologists like Hawking are adept at proving mathematical theorems about pseudo-Riemannian manifolds, see e.g. work on the chronology protection conjecture. Physical insights by Mandelbrot and Feigenbaum in 1970s led to the modern theory of fractals and chaotic dynamical systems. Perelman's work on the Ricci flow and the geometrization conjecture was as driven by physical inspiration as was Riemann's, one of the central notions in his proof is a new kind of entropy in a statistical canonical ensemble.
Perhaps the best evidence for the link is the 1990s controversy, where some mathematicians became concerned that the link between mathematics and physics became so strong that it was undermining the integrity of mathematics by blurring the lines between mathematical and physical "levels of rigor", and threatening to make mathematical results unreliable. The controversy was sparked by Jaffe and Quinn, who sugested explicit separation of "theoretical mathematics" with lowered standars of rigor, from the body of mathematics proper. Take a look at responses from who's who in modern mathematical physics: Atiyah, Glimm, Maclane, Mandelbrot, Thom, Uhlenbeck, Witten, etc.