Several highly unusual encounters with the earth's magnetopause occurred during an ~5-hour period on November 22--23, 1979, when the ISEE 1 and 2 satellites were near orbit apogee (~22.2 RE) at ~0900 local time. These distant magnetopause crossings corresponded to a subsolar earth-magnetopause distance of ~20.4 RE and were associated with a drop in solar wind dynamic pressure to a value (~1.4¿10-10 dynes cm-2)~100 times lower than is typical. Accelerated plasma flows whose magnitude and direction were consistent with the predictions of reconnection theory were observed on each of several satellite enecounters with the magnetopause and boundary layer during this 5-hour period. Further, the field variation through the magnetopause layer suggest that the magnetopause had the structure of a rotational discontinuity as required by reconnection theory. These observations thus indicate that on occasion reconnection at the dayside magnetopause can be a quasi-stationary process. Geomagnetic activity during this 5-hour period, and for at least 9 hours thereafter, was extremely low. Thus dayside reconnection is certainly not a sufficient condition for enhanced geomagnetic activity.