The wave number 4 (wave-4) and wave number 3 (wave-3) longitudinal structures in the thermospheric neutral mass density are understood as tidal structures driven by diurnal eastward-propagating zonal wave number 3 (DE3) and wave number 2 (DE2) tides, respectively. However, those structures have been identified using data from limited time periods, and the consistency and recurrence of those structures have not yet been examined using long-term observation data. We examine the persistence of those structures by analyzing the neutral mass density data for the years 2001-2008 taken by the CHAllenging Minisatellite Payload (CHAMP) satellite. During years of low solar activity, the amplitude of the wave-4 structure is pronounced during August and September, and the wave-4 phase shows a consistent eastward phase progression of $90^{circ}$ within 24 h local time in different months and years. During years of high solar activity, the wave-4 amplitude is small and does not show a distinctive annual pattern, but the tendency of the eastward phase shift at a rate of $90^{circ}$/24 h exists. Thus the DE3 signature in the wave-4 structure is considered as a persistent feature. The wave-3 structure is a weak feature in most months and years. The amplitude and phase of the wave-3 structure do not show a notable solar cycle dependence. Among the contributing tidal modes to the wave-3 structure, the DE2 amplitude is most pronounced. This result may suggest that the DE2 signature, although it is a weak signature, is a perceivable persistent feature in the thermosphere.