ZJX Controller described possible lost aircraft event that went unnoticed by the supervisory staff; allegedly due in part to their focus on time on position requirements; rather than operational responsibilities.

Narrative

Our facility management is still requiring 5 hours and 30 minutes on position each day. They are accomplishing this by opening sectors with no traffic and staffing unused positions. The managers are only focusing on maximizing time on position; and not sector needs. I was assigned to work the D side and traffic was starting to build. The Supervisor continued to put more Controllers on D sides at other sectors with no traffic. The Supervisor was not paying attention to our workload and we quickly became overwhelmed with multiple approaches and high altitude traffic. A VFR that we were providing flight following to went below our frequency and RADAR coverage; and we did not notice it because we were busy with the IFR traffic. The VFR disappeared from RADAR and we noticed it about 5 minutes later. We tried to relay to the aircraft; but did not have the time to do a full search since we were still busy. I tried to contact the Supervisor; but Supervisor was not even in the area. All of the controllers plugged in to the dead sectors were talking loudly and the distraction became overwhelming. The traffic slowed down long enough for me to give a briefing. The Supervisor was still not around; but the RADAR Controller continued to look for the aircraft. I took a 30 minute break and came back and a new Supervisor was in the area and assigned me to the same sector D side with a new RADAR Controller working. They still had not found the aircraft; but I assumed they were looking for him. The sector was still showing numerous tracks for the next several hours and we had not split it yet. Another Controller came back from break and I thought they were finally going to split the sector; and I saw they Supervisor send that Controller to sit on a D side of a sector with 3 aircraft. I called the Supervisor over and requested the sector be split by that Controller. He agreed and we split the sector. I then asked if they had found the previous VFR aircraft and the Supervisor looked at me puzzled. The Operations Manager was called and came down and said that since there was no flight plan outbound they did not know where to start looking for the plane. I would think landing airport would be a good place to start. So the RADAR Controller and I started to look for the plane on our own. I called the Airport Manager where the plane had come from and asked if the plane went back. The Controller confirmed that the aircraft landed 10 minutes ago; so we informed the Supervisor that we found the aircraft. Over an hour had passed since we initially lost radar contact with the aircraft and not a single management official had started a search. Fatigue and complacency are becoming rampant at this facility due to this time on position requirement. Managers are so distracted with keeping everyone on position for over an hour and a half; that they are not focusing on safety and running the areas.