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We present updated constraints on the free-streaming of warm dark matter (WDM) particles derived from an analysis of the Lyman-a flux power spectrum measured from high-resolution spectra of 25 z > 4 quasars obtained with the Keck High Resolution Echelle Spectrometer and the Magellan Inamori Kyocera Echelle spectrograph. We utilize a new suite of high-resolution hydrodynamical simulations that explore WDM masses of 1, 2 and 4 keV (assuming the WDM consists of thermal relics), along with different physically motivated thermal histories. We carefully address different sources of systematic error that may affect our final results and perform an analysis of the Lyman-a flux power with conservative error estimates. By using a method that samples the multidimensional astrophysical and cosmological parameter space, we obtain a lower limit mWDM a 3.3 keV (2 ɑ) for warm dark matter particles in the form of early decoupled thermal relics. Adding the Sloan Digital Sky Survey Lyman-a flux power spectrum does not improve this limit. Thermal relics of masses 1, 2 and 2.5 keVare disfavored by the data at about the 9σ, 4σ and 3σ C.L., respectively. Our analysis disfavors WDM models where there is a suppression in the linear matter power spectrum at (nonlinear) scales corresponding to k = 10h/Mpc which deviates more than 10% from a Lambda cold dark matter model. Given this limit, the corresponding "free-streaming mass" below which the mass function may be suppressed is ~2 X 108h-1Mo. There is thus very little room for a contribution of the free-streaming of WDM to the solution of what has been termed the small scale crisis of cold dark matter. [ABSTRACT FROM AUTHOR]