This paper is related to analysis of the Weddell Sea Anomaly (WSA) and the Mid-latitude Summer Nighttime Anomaly (MSNA) observed by the low altitude satellite DEMETER during nighttime between 2004 and 2010. This time interval corresponds to the decrease of the solar cycle 23 which was unusually long. It appears that, if these two anomalies have a peak in local summer (December in the Southern hemisphere for the WSA, June in the Northern hemisphere for the MSNA), the anomalies are also observed during the months around December and June with a decreased intensity. But at the end of the solar cycle 23 the summer peaks dramatically decrease and even relatively more quickly than the solar index F10.7. This phenomenon is much more significant for the WSA. It is shown that the mechanism producing the two anomalies (thermospheric neutral winds and magnetic declination effects) is strengthened by the solar ionization which is active during the night above the WSA and the MSNA areas. But at solar minimum, this mechanism is weakened. These results are valid at the satellite altitude (660 km) and may vary at lower altitudes.