Does immunodeficiency cause covid-19 failure?

Yes and no: If you mean vaccine failure, yes. But it depends on the kind of immunodeficiency. For example, people with HIV respond normally to the vacccine; whereas people with impaired antibody production (such as certain kinds of leukemia) may respond poorly. A "weak immune system" (e.g. someone who gets frequent colds) has no effect. If outwardly healthy, you can be sure the vaccine will work normally.

If you are immunosuppressed (cancer, chemotherapy, chronic illness, “autoimmune “ disease + many others) coronavirus vaccine will be less effective and coronavirus infection may be more severe. Many additional considerations, most of which are poorly understood