The influence on the conductance of armchair carbon nanotubes due to the presence of extended vacancy pairs has been investigated using a conventional pi-electron tight-binding model. It is found that the conductance in the linear band region around the Fermi energy contains resonance peaks and dips, which can be understood as double-barrier scattering resonances and Fano antiresonances and whose number depends on the longitudinal intervacancy separation. Furthermore, for a given longitudinal intervacancy separation, only two distinctly different conductance spectra appear in this energy region as the second vacancy in the pair assumes all different lateral positions around the tube circumference. It is also found that the conductance can be very sensitive to minimal changes in the relative intervacancy positions.