Well a little bit late but according to my knowledge (Pilot of a 737) they have to be recycled during the final phase of the circling approach because once you turn final and start descending towars the rwy the flight directors do not provide the wanted vertical and lateral profile comands (showing something different) -THIS IS A VISUAL SEGMENT. So if you recycle them they will be gone until if something gone wrong on the circl. app and you hit TO/GA they would pop out providing LAT and VERT info to guide you through the Missed approach. The same is in NPA flying LNAV/VNAV because before reaching FAF you set the MDH - 300ft below the Missed app alt you can set the actual missed approach altitude. If you kept the autopilot on down to MDH the FD would bring the plane to the Missed approach altitude.