The thermal instability of substitutional Ag doping on Cd sites in CdTe is studied with optical spectroscopy. For Ag doping levels above ${10}^{16}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ the ${\mathrm{Ag}}_{\mathrm{Cd}}$ concentration decreases gradually during several months while complex defects are formed, as evidenced by the evolution of low-temperature bound-exciton spectra. In particular, such a bound exciton (BE), ${X}_{2}^{\mathrm{Ag}}$, at 1.5815 eV has been studied in this work, as a typical example of complex Ag-related defects created in the course of release of Ag from Cd sites. A rich phonon spectrum is found to couple to this BE, as expected for a complex defect involving an interstitial species. Dye-laser-excited photoluminescence excitation (PLE) spectra reveal a single lowest BE state, with an orbitally excited (electron) state 8.6 meV higher. An activation energy of 8.8 meV is also found for the thermal quenching of the ${X}_{2}^{\mathrm{Ag}}$ PL emission, interpreted as an 1s-2s rate-limiting excitation of the electron in the BE, in good agreement with PLE data. Zeeman splitting of the 1.5815-eV ${X}_{2}^{\mathrm{Ag}}$ BE line is consistent with the assumption of an electron-hole pair bound to a neutral ``isoelectronic'' defect of a symmetry lower than tetrahedral. Further, the local potential of this defect is predominantly hole attractive, while the electron is loosely bound in a shallow donorlike state. The hole is a ${m}_{z}$=\ifmmode\pm\else\textpm\fi{}(3/2) state, as expected for an average tensional local strain field. A tentative identification is discussed in terms of a ${\mathrm{Ag}}_{\mathrm{Cd}}$-${\mathrm{Ag}}_{\mathrm{i}}$ pair, assumed to be produced by the spontaneous release of ${\mathrm{Ag}}_{\mathrm{Cd}}$ into interstitial (i) sites, with a rather high mobility of the ${\mathrm{Ag}}_{\mathrm{i}}$ interstitial also at room temperature. An alternative defect model, a pair of a Cd vacancy and an ${\mathrm{Ag}}_{\mathrm{i}}$ interstitial, cannot presently be excluded, however. A similar thermal instability of ${\mathrm{Cu}}_{\mathrm{Cd}}$ at a slightly higher doping level is found not to produce strong new BE spectra as for the ${\mathrm{Ag}}_{\mathrm{Cd}}$ case.