Brothers Orson West, 3, and Orrin West, 4, were reported missing on Dec. 21 in California City, Kern County, about 100 miles north of Los Angeles.
Jacqueline and Trezell West, their adoptive parents, said the boys vanished from the backyard, possibly roaming into the California desert.
"I saw them there, [I] went in the house, I came back out, I didn't seem them," Trezell West, the boys' adoptive father, told KERO-TV. "I realized that I left the gate opened, and I panicked, came inside the house, searched the house, me and my wife."
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Soon, authorities suspected foul play, according to California City Police Chief Jon Walker. Investigators believe the toddlers were taken and stress that the couple is not suspected in the case.
The reward, initially offered at $30,000 by extended members of the West family, has increased to $120,000 -- contributed by multiple parties.
Authorities have received more than 2,000 tips and are now using imaging devices at the adoptive parents' home to search for the boys.
No suspects or persons of interest have been named in the case at this time.
"We have not ruled anyone out," Walker said.
Meanwhile, the adoptive dad's family tells ABC News that they're targets -- not from authorities -- but from the public.
"It is misguided to blame uncles and aunts and grandparents for children who are missing that we love and care about and are trying to find," Watkins said.
"Right now there are people outside the home, talking about where are the boys," said Wanda West.
As the community continues holding vigils, the family is reminding everyone they're in deep pain too.
"It's like people don't realize we are grieving. We are hurting just like they are," Wanda West said.
The boys' biological mother blames their adoptive parents.
"They did something. I feel like they did something and they know something," Ryan Dean said.
The Wests said they understand her anger.
"I would think the same thing ... all I want is to find our babies," Trezell West said.
An investigation into the boys' disappearance remains active.
Walker said police requested polygraph tests for "multiple people."
"We haven't given up. We're still trying," he said.
ABC News contributed to this report.