Scipy curve_fit and method "dogbox"
I can't speak to the dogbox algorithm,  but the sigmoid only has range (0,1), so fitting to your example data is sure to be bad. The paper you reference presumably scales the input first.

The first example you give has a best fit that's a step function  which can be approximated by the sigmoid with parameters going to infinity; so it's no surprise the algorithm wouldn't converge. 

EDIT: Maybe you should try increasing the tolerances (passed as kwargs through curve_fit to least_squares); your error message mentions gtol specifically:  https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.least_squares.html#scipy.optimize.least_squares
Or, if things are converging enough for your purposes, just catch and handle that error?