Intensive theoretical and experimental efforts over the past decade have aimed at explaining the discrepancy between data for the proton electric to magnetic form factor ratio, $G_{E}/G_{M}$, obtained separately from cross section and polarization transfer measurements. One possible explanation for this difference is a two-photon-exchange (TPEX) contribution. In an effort to search for effects beyond the one-photon-exchange or Born approximation, we report measurements of polarization transfer observables in the elastic $H(vec{e},evec{p})$ reaction for three different beam energies at a fixed squared momentum transfer $Q^2 = 2.5$ GeV$^2$, spanning a wide range of the virtual photon polarization parameter, $epsilon$. From these measured polarization observables, we have obtained separately the ratio $R$, which equals $mu_p G_{E}/G_{M}$ in the Born approximation, and the longitudinal polarization transfer component $P_ell$, with statistical and systematic uncertainties of $Delta R approx pm 0.01 mbox{(stat)} pm 0.013 mbox{(syst)}$ and $Delta P_ell/P^{Born}_{ell} approx pm 0.006 mbox{(stat)}pm 0.01 mbox{(syst)}$. The ratio $R$ is found to be independent of $epsilon$ at the 1.5% level, while the $epsilon$ dependence of $P_ell$ shows an enhancement of $(2.3 pm 0.6) %$ relative to the Born approximation at large $epsilon$.
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