A man walked into a Jack in the Box on Monday and shot Joseph Gilbert Solano in the head

LOS ANGELES — A Los Angeles County sheriff's deputy who was shot in an off-duty attack at a fast-food restaurant died Wednesday, the sheriff announced.

Joseph Gilbert Solano, who had been on life support, died Wednesday afternoon, Sheriff Alex Villanueva.

Medical staff worked around the clock for two days "trying to do a miracle but unfortunately that didn't come to pass," he said.

A man walked into a Jack in the Box in suburban Alhambra on Monday and shot Solano in the head as he was waiting for his food order at the counter, authorities said.

Solano was out of uniform and there's no indication that the gunman knew he was a deputy, Villanueva said.

"The deputy was alerted in the restaurant that someone was following him and that's when he turned to confront it and that's when the shooting happened," the sheriff said. "But a motive or rationale from the suspect, that's the million-dollar question."

Solano's son, girlfriend, mother and other family members were at the hospital news conference.

"He was a really good dad," said his weeping son, Matthew Solano. "Continue to pray for him and my family, please."

Rhett Nelson, 30, of St. George, Utah, was arrested Tuesday on suspicion of the killing after he called his father in Utah from a Long Beach church to say he had killed someone.

Nelson's family has said he suffers from mental illness and an opiate addiction. It wasn't immediately known if he had a lawyer who could speak on his behalf.

Investigators said Nelson also is suspected of shooting a 30-year-old man standing on a Los Angeles street about an hour before Solano was killed. Both shootings appeared unprovoked and may have been random, authorities said.

Meanwhile, the San Diego Police Department, the San Diego County Sheriff's Department and the Carlsbad Police Department issued a news release Wednesday saying that Nelson is being investigated in connection with a series of five armed robberies of convenience stores that occurred in the area June 7 through Sunday.

In each robbery, the suspect wielded a handgun and demanded cash, the release stated. The crimes occurred in San Diego, Lemon Grove and Carlsbad.

Before the possible string of crimes began, however, Nelson's family contacted St. George police on May 27 and said he'd left their Utah home "without any specific reason" with a gun but they did not think he was suicidal or a danger to anyone else, Capt. Mike Giles said.

"He made a statement to them or somehow communicated he wanted to make it on his own or die," Giles said. They formally reported him missing the next day and said they believed the gun was for self-defense. It was not immediately known who owned the weapon.

Nelson has a history of mental illness and a history of opiate abuse, though he had been clean for about six months, according to statements from his father, Bradley Nelson. The family is "devastated beyond words" by the attacks and is cooperating with authorities.

"We believe we made every effort to help Rhett and bring him home safely without harm to himself or others, but despite our best efforts we were unable to locate him before this horrific act," the statement said.

On June 4, Nelson called his family from Rancho Santa Margarita in Orange County, Giles said. They still believed he was safe and police removed him from a missing persons database the next day.

On Wednesday, the Los Angeles County Sheriff's Department released Nelson's booking photo as part of an effort to seek any additional victims. Homicide investigators believe he may have been involved in other crimes in California.

Giles said no recent crimes involving Nelson have been reported to St. George police.

The Salt Lake Tribune reported that Nelson didn't have a violent criminal history in Utah but had previously pleaded guilty to driving with a "measurable amount" of a controlled substance in his body and guilty to underage alcohol offenses.

Los Angeles authorities recovered a gun from Nelson's car. It was not immediately clear if it was the firearm from Utah.