Stable ^{205}Tl ions have the lowest known energy threshold for capturing electron neutrinos (ν_{e}) of E_{ν_{e}}≥50.6 keV. The Lorandite Experiment (LOREX), proposed in the 1980s, aims at obtaining the longtime averaged solar neutrino flux by utilizing natural deposits of Tl-bearing lorandite ores. To determine the ν_{e} capture cross section, it is required to know the strength of the weak transition connecting the ground state of ^{205}Tl and the 2.3 keV first excited state in ^{205}Pb. The only way to experimentally address this transition is to measure the bound-state beta decay (β_{b}) of fully ionized ^{205}Tl^{81+} ions. After three decades of meticulous preparation, the half-life of the β_{b} decay of ^{205}Tl^{81+} has been measured to be 291_{-27}^{+33} days using the Experimental Storage Ring (ESR) at GSI, Darmstadt. The longer measured half-life compared to theoretical estimates reduces the expected signal-to-noise ratio in the LOREX, thus challenging its feasibility.