On Dec. 19, even before this year’s Axa Liberty Bowl is played New Year’s Eve, the game’s title sponsor, Axa Financial Inc., a New York financial services firm, announced it was ending its seven-year sponsorship, with AutoZone Inc., assuming it next year.

“Our business strategy did not allow us to create a long-term sponsorship,” said Axa spokesman Jeff Tolvin.

Likewise, Nathan Christian, a regional president for Wells Fargo & Co., said his institution is dumping its sponsorship of the Sun Bowl in El Paso after eight years.

“We did it in the first place, primarily as community support, at a time when the bowl was on the lip of the grave,” said Christian, who lived in El Paso for 22 years before moving to Southern California.

“We’ve had a very good experience with our title sponsorship. But a sponsorship has a life cycle. This has pretty much run its natural life cycle, like all advertising campaigns.”

Osram Sylvania Inc., the Danvers, Mass., lighting company, reached that conclusion after a run as sponsor of the Alamo Bowl in San Antonio from 1999 to 2001.

“When you got off the plane, there was no question it was the Sylvania Alamo Bowl, with signs everywhere,” said Michael Colotti, the firm’s vice president for brand management.

The problem, he said, was that Sylvania couldn’t get enough people, especially decision-making executives, to fly to San Antonio for the game and related events because it falls between Christmas and New Year’s.