Actually it was only off air for a year before it returned.
Wikipedia says the final original Rainbow went out in March 1992, and the first new one in January 1994, so nearly 2 years. I imagine repeats were shown in the interim though.
I imagine the retooling wouldn't have happened without the franchise change.
Rainbow was shown until Christmas 1992 in its original form when (I think) Tots TV took over its lunchtime slot in January 1993.
As far as I know there was no more editions of the original Rainbow aired until its new format was aired in January 1994 with Geoffrey axed. No singing from Rod, Jane and Freddy. A new puppet called Cleo was introduced. Zippy, George and Bungle had a makeover with Zippy and George now gaining an arm each.