Long-lived rovibrational states of the metastable D2-molecular anion, with lifetimes of the order of microseconds, were studied by recording the time-of-flight difference between D and D-fragments produced by spontaneous dissociation of the D2-complex. The simulated time-of-flight spectrum was adjusted to the experimental results, allowing us to extract the resonance energy relative to the dissociation threshold. A single value was found, 22.8 +/- 0.3 meV, which is somewhat larger than resonance energies predicted by theory for long-lived D2-rovibrational states with (J, v) quantum numbers (37,0), (37,1), and (38,0) [ Phys. Rev. A 75, 012507 (2007)]. This discrepancy seems due to the extreme sensitivity of thesemetastable states tominute features of the potential energy curve. The spectral feature is explained by the competition between autodetachment and spontaneous dissociation decay channels.