This paper shows that the long-term activity of the intermediate polar (IP) V1223 Sgr contains
clusters of the low-state episodes, sometimes even with a well-defined recurrence time. This can
be caused by a migration of star spots through the L1 point because of the differential rotation
of the donor. Large decreases of intensity in the 15-50 keV X-ray band accompany the optical
relatively shallow low states of V1223 Sgr. These X-ray variations are thus the results of the
decreases of the mass inflow rate to the disk from the donor. Absolute optical magnitudes $M_O$
of IPs show that most of these systems lie between those of dwarf novae (DNe) in outburst and
quiescence, so their disks are exposed to a thermal-viscous instability (TVI). The value of $M_O$
of V1223 Sgr in the high state is one of the brightest among IPs and is close to that of DNe in
outburst. This suggests that the disk of V1223 Sgr is in the hot (ionized) state. The values of $M_O$
of the IPs V426 Oph and TV Col lie in the region in which a TVI should be present. Indeed, the
optical brightness of V426 Oph is highly unstable on superorbital timescales. Short outbursts with
similar decay rates start from a highly variable baseline level. TV Col shows a gradual evolution
of brightness on timescale of hundreds of days. The outbursts shorter than a day are superimposed
on it. GK Per with a very long orbital period shows long dwarf-nova outbursts with the rise of the
optical intensity accompanied by a brightening in the hard X-ray band.