Helioseismology requires continuous measurements of very long duration, months to years. This paper addresses the specific and limited case of full disk measurements of p-mode oscillations, although it can be generalized, to some extent, to the case of imaged helioseismology. First, a method of mode by mode (or rather pair of modes by pair of modes) interpolation of the signal in gaps is tested, and shown to be efficient for gaps as long as two days, but limited to the frequency range where the signal to noise ratio is good. It is then noted that the autocorrelation function of the full disk signal, after dropping quickly to zero in 20 or 30 minutes, shows secondary quasi periodic bumps, due to the quasi-periodicity of the peak distribution in the Fourier spectrum. The first of these bumps, at 4 hours or so, is higher than 70 percent and climbs to nearly 90 percent in limited frequency ranges. This suggests that an easy gap filling method can be developed, with a confidence of nearly 90 percent across all the frequency range, as long as the gap does not exceed 8 hours, with at least 4 hours of data at both ends. Even a short gap of one or two periods is better filled by the data taken 4 hours earlier or later than by local interpolation. This relaxes quite considerably the requirement of continuity of the observations for the case the full disk p-mode helioseismology. Applied to 7 years of IRIS data, this method permits the detection of all low frequency p-modes already seen by 2 years of the GOLF instrument data, and makes possible the measurement of their frequencies with an accuracy consistent with the partially filled 7 years of statistics.