In September, professor Zeev Rothstein, the hospital's director general, gave a rare interview to Israel's Army Radio.
"He can move his eyes or a finger or a few fingers, that sort of reaction. … He reacts to pain, to the voice of a family member. These reactions suggest he is not completely unconscious but conscious at a very basic level. It is hard to say what he understands or what he does not understand. He does react to stimuli but this is nothing new," Rothstein said.
Sharon's demise has left a huge hole in Israeli politics and in the lives of those who worked with him.
Gissen used to read the newspapers to Sharon every morning at 5 a.m. to brief him on the day's developments at home and abroad.
"It's a great void," he said. "I try to fill the time, but it's just not the same without him."
Gissen also believes Sharon's disappearance has left a regrettable void in Israel's political life.
"Sharon was a real leader. The real predicament of his absence is that he left no obvious heir. Right now it would be good to have someone of his stature to lead us, to guide us," he said.
As to Sharon's physical condition and the state of his body, Rothstein said, "A patient who has spent such a long time on a hospital bed will never look the same as he looked as he was up and running. So he looks different."
Rothstein hasn't lost hope that Sharon will make progress but admits there has been no real recovery of brain function since the stroke.
For some the idea of Sharon lying in his current listless state raises difficult questions about whether or not he should be kept alive.
"It's up to the family," said Gissen. "He is still alive. If you stop feeding him, he will starve to death. That's against every Jewish law. There is still the slightest chance he may improve, although it's very unlikely. It's up to the family."
Gissen clearly misses his old boss. He said Sharon was one of the last "founding fathers of Israel," part of the generation of soldiers and politicians who helped establish the Jewish state in the 1940s. Despite their decades-long relationship, Gissen has chosen not to visit Sharon's hospital room.