"I thought I'd get well," he said, "but I never did."
It wasn't until a life-threatening infection developed in his bones that he finally relented: his lower right leg had to go.
Last winter, it was amputated.
And Frazier, a key figure in the Bruins' upset of top-ranked Ohio State in the 1976 Rose Bowl, braced for the crash.
It never came.
"I'm a new man in terms of not having that infected feeling, not being sick all the time," Frazier, 57, said from his home in University City, Mo., a lilt in his voice. "I'm still getting used to this prosthetic, but I'm doing better, babe. …
"A lot of people don't understand why I'm not depressed, but I feel so much better that I'm actually a happy camper."
Frazier, a regular on the 1980s HBO sitcom "1st & Ten," would be happier still if he could revive his acting career.
"I was an artist before I was a football player," said the former theater arts major, an actor, singer, writer and multi-instrumentalist. "I just happened to excel athletically and get a big name, but I was always an artist, man, always."
A native of Chesterfield, Mo., and a two-time All-American at Fort Scott Community College in Fort Scott, Kan., Frazier says he went to UCLA "because it gave me the best opportunity for both things I was interested in: athletics and the art world."
In 1975, he was an All-American for coach Dick Vermeil and the Bruins' defensive player of the year. The Bruins were crushed by Ohio State, 41-20, in an October game at the Coliseum, but eight weeks later they wrapped up their first Rose Bowl bid in 10 years by topping USC, 25-22, despite fumbling 11 times.
"Right then, I knew there was nobody in this country that could beat us," Frazier said. "We peaked at the right time."
Woody Hayes, in his last trip to the Rose Bowl, had an unbeaten Ohio State team that led the nation in scoring, ranked second in points given up and was a two-touchdown favorite over the 11th-ranked Bruins, who'd lost twice and tied once.
But UCLA dominated the second half of a 23-10 stunner, John Sciarra and Wendell Tyler leading the offense and Frazier sparking the defense with 13 solo tackles and an assist.
What happened at halftime to spark the turnaround?
"We just came in and ate a little raw meat," Frazier told Sports Illustrated, "and spread some gunpowder on everybody's dish."
Frazier laughs when the quote is read back to him 34 years later, noting, "I was just trying to be funny."
His athletic career had reached its high-water mark.
A second-round pick of the Kansas City Chiefs, he knew he faced a rough road when the Chiefs phoned him on draft day.
"They didn't say, 'Welcome to the Kansas City Chiefs,' " Frazier said. "They said, 'We hear you've got a bad attitude,' and it broke my heart. I said, 'What? Who told you that?' "
Lynn Stiles, UCLA's defensive coordinator under Vermeil, says Frazier was a "gamer" and a "first-round talent" who often frustrated his coaches by paying less than rapt attention in practice.
As a motivational tool, Stiles says, the UCLA staff enlisted a camera crew to train its lens on Frazier in the lead-up to the Rose Bowl, hoping to keep the lineman focused.
Nobody told Frazier that the camera was empty, Stiles notes, "and that might have been the best prepared he ever was going into a game. … He was extraordinary."
Frazier, though, didn't last long in the NFL.
He played in 14 games with the Chiefs, was unable to catch on with any other team and left football behind in 1978.
A year later, he landed his first film role, in "North Dallas Forty." A friend, Joe Sutton, put him to work as a record promoter after Frazier told him he'd like to learn the music business.
"He was always a little involved with acting, a little involved with music, a little involved with writing," said Sutton, whose long career in entertainment has included stints as a manager for Neil Diamond and Ricky Nelson, among others. "He never quite zeroed in, and in the entertainment business, you have to zero in."
Stardom may have eluded him, but Frazier seemed to be doing all right for himself. For several years in the 1980s, he was married to singer Thelma Houston, best known for her chart-topping 1977 disco hit, "Don't Leave Me This Way."
Later, with another woman, Frazier fathered a son, also named Cliff, who is a senior tennis player at Alabama State.
And from 1984 to 1991, in his longest-running acting role, he played the part of Jethro Snell in "1st & 10," about the on- and off-the-field hi-jinks of the fictional California Bulls football team.
Shortly after the show was canceled, Frazier was diagnosed with diabetes, kicking off a nearly two-decade battle with the disease.
"I'm not as agile as I'd like to be," he said, "but I'm hoping to get a new prosthetic in the next year. I'm happy I'm not going back to the hospital. I'm really very thankful. …
"I've got a new perspective on life."