Why reaginic antibodies are absent in these types of syphilis?
To make the diagnosis of syphilis, the most common tests fall in two categories :


Non-specific tests like VDRL test &amp; Rapid Plasma Reagin (RPR) test : those detect antibodies against cardiolipin, present in the treponema but also in our cells. 
Specific/treponemal tests like TPPA/TPHA &amp; FTA-ABS : antibodies titers against antigen specific to T. pallidum are  measured.


Non-specific titers decrease when antigenic stimulation ceases : either when syphilis is cured (no more treponema), or in the late stage where the number of bacteria present in non-immune-privileged zone is low (treponema is almost eliminated except in the central nervous system, eyes, testis where it is protected from immune response). 

Specific titers fall very slowly if at all, once they are acquired.

Thus in late stage syphilis we get the following : VDRL- TPHA+, a source of confusion since this can also indicate old/cured syphilis.