Suprathermal electrons focused along magnetic field lines, called the strahl, carry heat flux away from the Sun. Various factors can cause heat flux dropouts (HFDs), including times when the strahl almost vanishes. HFDs are a necessary but insufficient condition for detecting magnetic flux disconnected from the Sun. To quantitatively assess the fraction of HFDs which might be due to disconnected fields, we use four years of suprathermal electron data from the Wind spacecraft to perform a comprehensive survey of heat flux dropouts with durations greater than an hour. Eliminating periods within interplanetary coronal mass ejections or containing counterstreaming electrons, we find that only ~10% of HFDs have signatures consistent with disconnected flux.