In other words, there must be matter present in the Milky Way that we cannot see. Astronomers continued to look at this discrepancy. Year after year they refined the measurements. Another arguement for missing mass is the shape of the velocity rotation curve for the Milky Way. It is remarkably flat.
Many spiral galaxies have similar flat rotation curves.
There are many answers to this. Combining several potentials will work, especially when one of the forms is that of an approximately spherical shape where the density decreases outwards. Interestingly, there is a particular potential called the Mestel potential that also reproduces a flat rotation curve without the introduction of a halo. So a halo is certainly sufficient to produce a flat rotation curve but it is not necessary. Nature will do the right thing regardless of how we choose to map it.