We observe fragmentation of H2 molecules exposed to strong laser fields into excited neutral atoms. The measured excited neutral fragment spectrum resembles the ionic fragmentation spectrum including peaks due to bond softening and Coulomb explosion. To explain the occurrence of excited neutral fragments and their high kinetic energy, we argue that the recently investigated phenomenon of frustrated tunnel ionization is also at work in the neutralization of H+ ions into excited H atoms. In this process the tunneled electron does not gain enough drift energy from the laser field to escape the Coulomb potential and is recaptured. Calculation of classical trajectories as well as a correlated detection measurement of neutral excited H and H+ ions support the mechanism.