It is certainly possible that a negative test result to change to a positive, overtime. This is the basis, why health care providers ask patients to repeat the tests at a later date, to avoid missing a infected patient.
97% of normal individuals with a good immune system, produce antibodies within 4-12 weeks and the remaining (3%) might produce the antibodies, around or after 6 months.
I have mentioned the conditions, (that you have mentioned in the query above) which in case a person has, can have delayed antibody production, and hence will require repeated testing upto 6 months or more. It is in such patients that tests can become positive at a later date.
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