After Luke and Leia were born and Obi-Wan was watching Luke grow up on Tatooine, was he able to keep in touch with any of his old contacts? Especially with Bail Organa, who was raising Leia? Was he able to keep track of Leia's progress and growth while she was living on Aldaraan? Or was there anyone else he was able to communicate with? Or did he stay incommunicado?
Yes, and intentionally so
In the Disney canon novel Ahsoka, Bail Organa muses that Obi-Wan wished to avoid contact with him:
He debated sending a message to Obi-Wan but almost immediately dismissed the idea. They had agreed to no contact, except in the direst of emergencies, and as much as a Jedi survivor might make his old friend feel better, Bail knew it wasn’t worth the risk. Someday, if he had a reason to reach out, he would.
So Obi-Wan intentionally avoided contact with Bail and other former acquaintances for fear of discovery. The gaze of the Empire (and of the Emperor) was much heavier upon Bail, for example, than on Tatooine.
While Obi-Wan tried to avoid communicating with his friends, he was, as mentioned in the other answer, in communication with Qui-Gon’s force spirit.
Obi-Wan let go of Ben Kenobi’s house, the last place in the galaxy where a piece of Anakin Skywalker rested, and broke through the wall between life and death. It was dark there if he wanted to take anything with him or leave anything behind, but he wished for neither of those things, so he stood in the light. His senses were sharp. He could hear every sound at once, and also none of them. It took him a moment to focus on the voice he wanted most to hear.
Alone and connected. Aloof and hopelessly entwined. Obi-Wan had only a moment before he was wrenched back into the physical world, but it was long enough to renew his hope.
“Obi-Wan,” said Qui-Gon Jinn. He was sure the voice was stronger this time. “Let go.”
As an additional note, it seems likely, based on recent revelations from Star Wars: Rebels, that Obi-Wan will be revealed to have had some contact with
Darth Maul, now just Maul.
Not sure about the living, but he most certainly communicated to Qui-Gon's Force Spirit (when learning how to become one himself), and presumably Qui-Gon's Force Spirit was in contact with Yoda, so this was at least one channel.
First, we know that Obi-Wan was communicating with Qui-Gon Jinn on Tatooine. Second, the Emperor could sense "disturbances in the Force" which could also indicate that the more often that Obi-Wan used his Force powers, the more likely that his location might eventually be discovered by the Emperor. Once Obi-Wan received Leia's distress call from R2, he realized that he had to teach Luke the ways of the Force in order for the Rebel Alliance to have 'any chance' of defeating the Empire. So, I wouldn't say that Obi-Wan was "out of touch" with the people he knew, per se.