Serological assays measuring antibody response
Antibodies used for serological tests are performed in vitro, and are not required to be effective for eliminating the pathogen. For an infected individual, antibodies may play a role in neutralization, opsonization, or activating the complement system (checkout Janeway's Immunobiology for more details). There are a number of reasons why antibodies may be present and not trigger an effective response down these pathways.

For example, E. Coli O157:H7 produces Shiga toxin and there are immunoassays to test for the presence of the toxin in feces (1). Only low amounts of the toxin is needed to cause disease. Antibodies against the toxin have been seen in individuals with the disease, suggesting the toxin is not a strong enough challenge for an immune response Discussion of (2). 

You could go case-by-case for each of the immunoassays and see why their targets are difficult to turn into therapeutics.