Diffractive dissociation of virtual photons, γ*p → Xp, has been studied in ep interactions with the ZEUS detector at HERA. The data cover photon virtualities 0.17 < Q2 < 0.70 GeV2 and 3 < Q2 < 80 GeV2 with 3 < MX < 38 GeV, where MX is the mass of the hadronic final state. Diffractive events were selected by two methods: the first required the detection of the scattered proton in the ZEUS leading proton spectrometer (LPS); the second was based on the distribution of MX. The integrated luminosities of the low- and high-Q2 samples used in the LPS-based analysis are ≃ 0.9 pb-1 and ≃ 3.3 pb-1, respectively. The sample used for the MX-based analysis corresponds to an integrated luminosity of ≃ 6.2 pb-1. The dependence of the diffractive cross section on W, the virtual photon-proton centre-of-mass energy, and on Q2 is studied. In the low-Q2 range, the energy dependence is compatible with Regge theory and is used to determine the intercept of the Pomeron trajectory. The W dependence of the diffractive cross section exhibits no significant change from the low-Q2 to the high-Q2 region. In the low-Q2 range, little Q2 dependence is found, a significantly different behaviour from the rapidly falling cross section measured for Q2 > 3 GeV2. The ratio of the diffractive to the virtual photon-proton total cross section is studied as a function of W and Q2. Comparisons are made with a model based on perturbative QCD.