I saw a total of 15 Burns and Allen episodes during Antenna TV's marathon, 10 on Saturday and the final 5 of the marathon today. In all 10 yesterday George and Gracie's real life son Ronnie Burns wasn't seen at all or even mentioned. But he had a prominent part in today's episodes. Happy Days famously created the Chuck Cunningham syndrome, where missing children/siblings like Chuck Cunningham and Judy Winslow disappear without being mentioned again. Burns and Allen the opposite seems to be true, not mentioned at all for awhile then suddenly appearing like he was always part of the TV show.

A good observation!

While George would sometimes refer to Ronnie (and his sister Sandra) in monologues, neither of the Burns children were regulars on the show up to 1955. I think it was because of George and Gracie wanting them to have private lives-as well as the idea of them as preadults being raised by Gracie (the character) didn't seem as funny as how George, the Mortons and the other adults had to deal with Gracie!

However, I think George thought that Ronnie would help boost the ratings among the teens so that's why he was brought in (as a 'college student) but he sure seemed strangely awkward and even unfunny compared to his dry humored dad and wacky mom. He sure didn't seem as though he'd have actually been raised by them in character (yes, I know that Gracie was far more intelligent and strict offstage than she let on via her character).

Ronnie had an early appearance or two before the sixth season (when he got the regular role as himself), but he was playing other small roles. George mentioned him at the end of one episode.

Sandra had varying small roles throughout the series.

IIRC both were adopted by the Burnses.