What is Rukia? A shinigami. Renji? A shinigami. I'll exclude the other Shinigami stince they are not that close with Ichigo.
Now, what is Ichigo? He was a Shinigami (Substitute), but after losing his power he is just a normal human.
Does normal human communicate with Shinigami? No, they are not supposed to. Since Ichigo is a normal human after losing his power, he and Rukia are not supposed to communicate with one another. Sure they can communicate if Rukia wears a gigai, but being a Shinigami and a Kuchiki, Rukia chose not to. Renji is a Vice-Captain, so him using a gigai to visit Ichigo every now and then would set a bad example for other Shinigami. This is the first reason, Shinigami and human are not supposed to be communicating with one another.
Another reason is that a that time, the great crisis Aizen "God" Sousuke was overcame mainly due to Ichigo's contribution. He was the one who weakened Aizen enough for the sealing kido created by Urahara to work. He has contributed more than enough in this battle. So, as a veteran, now that he lost his power and considering that he was only 17 at that time, it is perfectly understandable that the Shinigami would want Ichigo to finally have a peaceful life befitting of a human.
With those two reasons, it is perfectly understandable that Rukia and Ichigo parted ways there.
Also, do not forget that normally those assigned to the human world are non-seated Shinigami. Renji is a seated officer. Rukia was not but she got promoted soon after. For seated officers to visit the human world, they would need to pass a certain gate where they would have a seal applied to them which would restrict their power. This procedure requires them to fill a paperwork beforehand. If they were to use this for personal reason (visiting a friend), people would have a bad impression of them, thinking that they are using their position for their own personal needs (nepotism).