What can I expect from a fixative?
Yes, it is absolutely possible to completely fixate the pigment on its support, but there is a lot of difference in quality between brands and purposes. So, yes, you probably have a low-quality or inappropriate one - assuming your support is not wet or too smooth, which can both impede the fixation.
A couple of coatings is usually the recommended application. Apply the fixative evenly, about 30 cm perpendicular to the paper.
I stumbled upon this blog post on jacksonart.org with an extensive comparison of several brands and types, offering information and insight in the process.