Gnuplot's fit command is fairly robust, but when asked to fit with parameters that differ in size by many orders of magnitude, the fit command fails.
While it's easy enough rescale a function so that the parameters are of similar magnitude, it isn't always obvious that this is necessary. But this can be done internally to the fit command.
I've attached a patch that touches 7 lines and adds 13 more to fit.c that does this. I've tested this on some data sets where the scaling problem arises, and also on the fits in fit.dem. If reasonable initial guesses are provided, the fits often (but not always) seem to converge in fewer iterations.