Problems with large variations in coefficients are often described as stiff. You can think of it as a problem with several things happening, but with very rapid transients compared to the other components.
Those problems tend to cause ODE45 to stall. It will try to make the time step EXTREMELY small, since ODE45 is an adaptive solver. But when the time step goes essentially to zero, and still no success, guess what happens? So when I see a problem that someone says has stalled, AND it has large variations in coefficients, the odds are good that it is stiff.
The easiest test of this assertion is to use a stiff solver instead. So use one of the ODE suite of tools that ends in an s instead of ODE45.
