After caucusing for about an hour Thursday, the 25-member Assembly Republican Caucus voted nearly unanimously not to replace the Tulare Republican who has held the top post for two years.
A motion to vacate the chair received only one vote, two members said privately. Caucus sessions are held behind closed doors.
Conway, who is termed out of the Legislature next year, leads a caucus still reeling from the loss of three seats in last November's election, a stunning party defeat that handed Democrats a supermajority in the 80-member house.
But President Barack Obama's decisive victory in California and statewide redrawing of political districts tended to favor Democrats in other political races as well -- the GOP lost two state Senate seats, for example.
Conway replaced Assemblyman Martin Garrick, of Solana Beach, as Assembly GOP boss in November 2010. She became the fourth Republican leader of the lower house in an 18-month period. Garrick opted not to seek a second term as caucus chief.
PHOTO CREDIT: Assembly Republican leader Connie Conway, R-Tulare, during the first day of session at the state Capitol in Sacramento on Monday, Dec. 3, 2012. Hector Amezcua / Sacramento Bee