We report on spatiotemporal evolution of relativistically intense longitudinal electron plasma waves in a cold homogeneous plasma, using the physically appealing Dawson sheet model. Calculations presented here in the weakly relativistic limit clearly show that under very general initial conditions, a relativistic wave will always phase mix and eventually break at arbitrarily low amplitudes, in a time scale omegapetaumix approximately {3/64(omegape2delta3/c2k2)|Deltak/k|(|1+Deltak/k|)](1+1|1+Deltak/k|)}(-1). We have verified this scaling with respect to amplitude of perturbation delta and width of the spectrum (Deltakk) using numerical simulations. This result may be of relevance to ultrashort, ultraintense laser pulse-plasma interaction experiments where relativistically intense waves are excited.