Ultraviolet and visible photodissociation of a vibrationally excited HT ion beam, as produced by standard ion sources, was successfully implemented in an ion storage ring with the aim of investigating the decay of the excited molecular levels. A collinear beams configuration was used to measure the photodissociation of H-3(+) into H-2(+) + H fragments by transitions into the first excited singlet state with 266 and 532 nm laser beams. A clear signal could be observed up to 5 ms of storage, indicating that enough highly excited rovibrational states survive on the millisecond time scale of the experiment. The decay into H-2(+) + H shows an effective time constant between about 1 and 1.5 ms. The initial photodissociating states are estimated to lie roughly 1 eV below the dissociation limit of 4.4 eV. The expected low population of these levels gives rise to an effective cross section of several 10(-20) cm(2) for ultraviolet and some 10(-21) cm(2) for visible light. For using multistep resonant dissociation schemes to monitor rotational populations of cold H-3(+) in low-density environments, these measurements open promising perspectives.