Yes HIV tests detect antibodies, that is the only approved test for diagnostic purposes is an antibody test.
No they will never disappear
No...3 months post exposure
Your test at 4 months will cover anything there and back
An HIV test should cover 3 months following exposure. HIV antibodies NEVER disappear from the bloodstream. If a person was to be infected with HIV, the virus would make copies of itself in the body everyday, so our body's immune system would respond everyday as a result.
I have also had someone tell me that it is possible for HIV to go undetected for years. This is regarded as a myth.
According to the San Francisco AIDS Foundation:
"The three month window period is normal for most of the population. Many people will have detectable antibodies in three or four weeks. Very, very rarely (i.e., only a few cases ever), a person could take six months to produce antibodies."
So be happy, for it is my belief that you are A-OK! :)