Badly approximable infinite products of quadratic polynomials

We provide a number of conditions on the rational numbers $u$ and $v$ which ensure that the Laurent series $g_{u,v}(x):={\prod }_{t=0}^{\mathrm{\infty }}(1+u{x}^{-3^t}+v{x}^{-2\cdot 3^t})$ is badly approximable.