It's presumed Kochin was once mentally stable, though this was never really mentioned. After saving Dr. Wheelo's life by placing his brain in a glass container after being diagnosed with lung cancer, he left to buy groceries. Without a means of transportation, it is assumed this took a very long time. However, once he came back, he found that the lab had been completely iced over. He tried everything he could think of to get rid of the ice, but that only made things worse.
In an act of desperation, Kochin set out to find the Dragon Balls. After searching for 50 years, Kochin was finally able to summon Shenron and wish for him to melt the ice. Once reunited with Wheelo, he promised he would get him the body of the world's strongest warrior despite Dr. Wheelo simply just wanting any body he could get.
It's possible that Kochin went insane within the 50 years he was searching for the Dragon Balls. Searching the entire globe, looking for each individual Dragon Ball without a radar might have frustrated him to the point of losing his mind causing him to forget why he wanted to reunite with Wheelo in the first place, but another explanation might just be that he's losing his marbles due to dementia.