30 Rock's core was actually family. Each of the main characters got the opportunity to explore their unique and sometimes troubled relationships with their families, often on a deeply personal level. There was usually some sort of resolution to these stories, with one notable exception. Liz Lemon's brother Mitch went through something horrible, and it was never really resolved.
Liz's family first appeared in Season 2, Episode 9. They came up to New York to visit Liz over Christmas, introducing fans to the rest of the Lemons. Her parents Dick and Margaret Lemon came across as classic Midwestern residents and were incredibly supportive of their daughter. But her brother Mitch was an entirely different story given his exceedingly unique condition.
In high school, Mitch went on a class skiing trip that unfortunately took a bad turn. He sustained a brain injury that caused him to wake up everyday thinking it was December 7, 1985. While Mitch was in fact 40 years old, he believed he was still 17 and heading out on the big ski trip the next day. His family did everything they could to maintain the illusion so that they wouldn't traumatize him.
While Mitch only appeared in this one 30 Rock episode, he was referenced prior to his appearance. This was done to set up his trauma-induced Nivea aphasia. It was also heavily implied that Jenna had a sexual relationship with him at some point. Due to his condition, Mitch didn't remember that happening, something that absolutely drove Jenna nuts as she prided herself on being memorable, if nothing else.
Unfortunately for the Lemons, Colleen Donaghy was in town. She decided to prove to Jack Donaghy that the Lemons were not as happy as they pretended to be. She pushed until their house of cards collapsed. Part of the aftermath was Mitch seemingly getting his memories back. He suddenly realized how old he was and how much time he had lost. But that was the end of his journey on the series.
30 Rock never followed up with Mitch after that. He easily could have woken up the next day and forgotten about his encounter with Colleen, thanks to his condition. Jack would have been jealous of that since he had been trying to forget Colleen for years. However, if he remained in his mentally youthful state, one has to wonder where Mitch would have ended up. Liz certainly didn't seem to be planning for a future where she had to care for her brother.
But the other possibility might be even sadder. It's also possible that the trauma of finding out how much time he missed forcibly pulled Mitch out of his state. In that case, Mitch might have been left wondering why his parents chose to coddle him for 23 years instead of playing it straight with him. They might have been able to help Mitch sooner. Once he realized that, a rift with his family may have formed.
Since 30 Rock never re-visited Mitch Lemon or provided an update on his condition before the series concluded, it's impossible to know what happened to him. The reality of his unique situation was that both options had some serious downsides. While Liz's parents continued to be a presence in the series, Mitch would never be heard from again, leaving his fate a major loose end.