First measurements are presented of the diffractive cross section sigma(ep) -} eXY at centre-of-mass energies root s of 225 and 252 GeV, together with a precise new measurement at root s of 319 GeV, using data taken with the H1 detector in the years 2006 and 2007. Together with previous H1 data at root s of 301 GeV, the measurements are used to extract the diffractive longitudinal structure function F(L)(D) in the range of photon virtualities 4.0 {= Q(2) {= 44.0 GeV(2) and fractional proton longitudinal momentum loss 5 x 10(-4) {= x(P) {= 3 x 10(-3).