An analysis of ${K}^{0}$ regeneration data from Fermilab in the energy range 30-110 GeV has been carried out to determine the ${K}_{L}\ensuremath{-}{K}_{S}$ mass difference $\ensuremath{\Delta}m$, the ${K}_{S}$ lifetime ${\ensuremath{\tau}}_{S}$, and the $\mathrm{CP}$-violation parameter ${\ensuremath{\eta}}_{+\ensuremath{-}}$. We find that the average values of $\ensuremath{\Delta}m$, ${\ensuremath{\tau}}_{S}$, ${tan\ensuremath{\varphi}}_{+\ensuremath{-}}$, and $|{\ensuremath{\eta}}_{+\ensuremath{-}}|$ at Fermilab energies differ from the accepted low-energy (\ensuremath{\sim}5 GeV) values by approximately 4, 2, 3, and 9 standard deviations, respectively. As a consequence of the discrepancy between low-energy and high-energy values, an investigation of a possible energy dependence of the parameters was carried out. Using two different methods, the parameters were fitted to a form $x={x}_{0}(1+{b}_{x}^{(N)}{\ensuremath{\gamma}}^{N})$ where $x$ is any of the parameters $\ensuremath{\Delta}m$, ${\ensuremath{\tau}}_{S}$, $|{\ensuremath{\eta}}_{+\ensuremath{-}}|$, and ${tan\ensuremath{\varphi}}_{+\ensuremath{-}}$, $\ensuremath{\gamma}=\frac{{E}_{K}}{{m}_{K}}$ is the usual relativistic factor, and $N=1 or 2$. The resulting slope parameters ${b}_{x}^{(N)}$ differ from zero by 0-4 standard deviations depending on the parameter and on whether the low-energy value is included. The details of the fits are presented here, and a discussion is also given of new experiments which could check and extend the present results.