A wide range of analytes adsorb irreversibly to the surfaces of single walled carbon nanotube electronic networks typically used as sensors or thin-film transistors, although to date, the mechanism is not understood. Using thionyl chloride as a model electron-withdrawing adsorbate, we show that reversible adsorption sites can be created on the nanotube array via noncovalent functionalization with amine-terminated molecules of pK(a) < 8.8. A nanotube network comprising single, largely unbundled nanotubes, near the electronic percolation threshold is required for the effective conversion to a reversibly binding array. By examining 11 types of amine-containing molecules, we show that analyte adsorption is largely affected by the basicity (pK(b)) of surface groups. The binding energy of the analyte is apparently reduced by its adsorption on the surface chemical groups instead of directly on the SWNT array itself. This mediated adsorption mechanism is supported by X-ray photoelectron spectroscopy (XPS) and molecular potential calculations. Reversible detection with no active regeneration at the parts-per-trillion level is demonstrated for the first time by creating a higher adsorption site density with a polymer amine, such as polyethyleneimine (PEI). Last, we demonstrate that this transition to reversibility upon surface functionalization is a general phenomenon.