Two-year-old Aisling has not been seen since about 5.30pm on Monday in Longburn Rd, Henderson.
Police have been unable to find Aisling and now believe it is likely she has been abducted.
Aisling's mother Angela was unable to keep her emotions in check, holding her husband Alan close as he spoke about their lives since Aisling disappeared.
"The last few days have proved to be the most harrowing of our lives," Mr Symes said.
"We have had no sleep and feel like we are barely existing."
It had been very difficult not knowing where Aisling was, Mr Symes said.
"We want her back, so please, if you have any information, anything at all, please come forward."
Mrs Symes could be heard breaking out into tears shortly after the press conference ended.
Investigation head Inspector Gary Davey said police now had about 40 people on their criminal investigation team.
He urged anyone who had Aisling to ensure she was returned home safely, either by coming to police or dropping her off at a safe point.
