Proton spin-lattice relaxation times (${T}_{1}$) measured for the first time across a random transition-metal alloy system, ${\mathrm{V}}_{\mathrm{x}}$${\mathrm{Nb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{H}}_{0.2}$, from 100 to 700 K reveal (a) a suppression of hydride phase precipitation at low temperatures accompanied by enhanced retention of hydrogen in the solid-solution (\ensuremath{\alpha}) phase compared to pure V or Nb, (b) hydrogen motion in the \ensuremath{\alpha} phase at intermediate compositions governed by a distribution of activation energies, and (c) a transition to short, almost temperature-independent, ${T}_{1}$ behavior in \ensuremath{\alpha}-${\mathrm{V}}_{0.1}$${\mathrm{Nb}}_{0.9}$${\mathrm{N}}_{0.2}$ consistent with localized hydrogen motion around attracting V atoms.