What is it, LLC type? The first L's energy decays in less than a cycle, returning to the supply. The LC tank rings down, if still having more amplitude than the supply then it also discharges into the supply partially. The leftover rings down gradually. It may ring down incompletely before the next pulse starts (if pulse skipping / burst mode control is used), in which case some energy may be returned; or more energy may be consumed if the pulse is out of phase with the ringdown.
I think you will find, for typical, recommended values, the amount of energy lost is quite small, so it's quite easy to tolerate such losses on an infrequent basis. The efficiency may not be fantastic, but the absolute power loss needn't be.
Consider a tank delivering 100W output power, with 100VA reactive power, made with components giving a total Q of 100. Every cycle, 1W of that reactive power is dissipated as heat and when it's turned off, it rings for, roughly 100 cycles (give or take what time constant you consider it "done" ringing). If the control restarts within say 10 cycles, not much energy will have been lost. If more than 100, then ~all the energy in the tank is gone. If Fo is 100kHz, the resonant energy is VAR / (2*pi*Fo) = 160uJ, and if the pulse rate is 1kHz then the dissipation is all of 0.16W, a fraction of the continuous-duty losses.
If you're only delivering 1W at that condition, your efficiency is less than 86% (compared to < 99% at nominal load), pretty pitiful, but that's a lot to expect of dynamic range to expect from a power supply and I would suggest be less picky.

Tim