It's actually pretty similar to how many comedy partnerships broke up and then got back together. Abbott and Costello had an acrimonious breakup in 1955, got back together, and then formally dissolved their act again in 1957. Costello went solo doing standup and he even had a guest spot on the long running western TV series Wagon Train before his death in 1959. Abbott, meanwhile teamed up for a time with Candy Candido (whose distinctive guttural growl you've heard if you've ever watched several classic Disney films) and even did his own voice in 156 five minute Hanna-Barbera cartoons featuring bits that he did with Costello (who was voiced by Stan Irwin).
Then of course there was the famously bitter breakup between Dean Martin and Jerry Lewis (who had replaced Abbott and Costello as the most popular double act in the US), which this manga seems to be emulating. Right at the end before their breakup, Martin even told Lewis, "You're nothing to me but a fucking dollar sign." (Similar to the line Suberta says to Koronta) After their split, they didn't speak to each other for four years and didn't reconcile fully for another 20 years, but they did in fact perform together again a few times, the last time in 1989 at a show in Las Vegas for Martin's 72nd birthday. So, it does happen.