Why did the patients visit Dr. Raman only when they were hopeless?

The patients visited Dr. Raman only when things looked hopeless because they couldn't afford his high fees and also because they felt that his presence would jinx their probability of survival.
Basically, these superstitious patients believed that Dr. Raman's presence at their bedside would result in certain death. It's a vicious cycle. First, patients neglected calling on Dr. Raman because they couldn't afford his fees. So, they usually waited until their cases were hopeless. Then, and only then, did they call on Dr. Raman, as a last-ditch effort to save themselves.
However, the time factor usually proved fatal: patients who waited too long to get the care they needed often died. Because Dr. Raman usually presided over these deaths, he began to get the unenviable reputation of being a sort of jinx.
We see this in the story, when Gopal's wife makes her excuses for not calling on Dr. Raman. Accordingly, Gopal has been bedridden for one and a half months. Gopal's wife is visibly embarrassed when Dr. Raman asks her why they have neglected to alert him to Gopal's condition. She stammers that neither she nor Gopal wanted to inconvenience Dr. Raman. However, the truth is that, like many others, they couldn't afford his fees and didn't want to jinx Gopal's chances of survival. Through denial, they had hoped to preserve the facade that Gopal was merely sick and not dying.

The story is set in the fictitious South Indian town of Malgudi, which provides the backdrop to most of Narayan's stories. Here, Dr. Raman has something of a reputation as someone you only call out when you're on your last legs. The reason is very simple—the good doctor does not come cheap. His visiting fee is the princely sum of twenty-five rupees, quite a lot of money in a small Indian town at that time. As most people in Malgudi are rather poor, they will only call the doctor as a last resort. As a consequence of this, the name of Dr. Raman has come to have a certain ominous ring to it; if you need to call him, then it's almost always a sign that you're in a bad way. Whenever the good doctor arrives on the scene, it's usually curtains for the poor, unfortunate patient.