Context. Stars on the asymptotic giant branch (AGB) are long-period variables that present strong flux variations at almost all wavelengths, including the SiO maser lines. The periods of these variations are of 300-500 days in Mira-type stars and somewhat shorter in semi-regular variables. The variability of the SiO lines on short timescales has been investigated, but the data are inconclusive. Aims. We aim to study the time evolution of the SiO maser lines in Mira-type and semi-regular variables at short timescales. We also discuss the origin of the observed fast variations. Methods. We observed the SiO maser lines at 7 mm (28SiO v=1,2 J=1-0) and 3 mm (28SiO v=1 J=2-1) using the 40 m Yebes antenna and the 30 m IRAM telescope, respectively, with a minimum spacing of 1 day. We studied the semi-regular variables RX Boo and RT Vir and the Mira-type variables U Her, R LMi, R Leo, and $chi$ Cyg. We performed a detailed statistical analysis of the variations on different timescales. Results. RX Boo shows strong and fast variations in the intensity of the different spectral features of the SiO lines at 7 mm and 3 mm. On a timescale of one day, we find variations of >10% in 25% of the cases. Variations of greater than $sim$50% are often found when the observations are separated by 2 or 3 days. A similar variation rate of the SiO lines at 7 mm is found for RT Vir, but the observations of this object are less complete. On the contrary, the variations of the SiO maser line intensity in the Mira-type variables are moderate, with typical variation rates around <10% in 7 days. This phenomenon can be explained by the presence of particularly small maser-emitting clumps in semi-regular variables, which would lead to a strong dependence of the intensity on the density variations due to the passage of shocks.
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