What are the parameter values? Are they fixed or e.g. optimized over?
This is an illustration of the Hill function from Wikipedia:
By D Wells - Own work, CC BY-SA 4.0, Link
For coefficients between 0 and 1 it does have the same problematic properties as the square root examples mentioned earlier (essentially an ill-defined derivative at some point, here at 0) that creates ambiguities in the (backward-time) solution and causes more issues further down the line (like negative concentrations).
So my guess is it all comes down to the value of the Hill coefficient n in your equations.
PS: I just wanted to drop this philosophical physics problem here, since I only recently learned about that. It asks what implications these mathematical properties have for Newtonian physics: Norton’s Dome