Ellie (8) was last seen in Dublin Airport in July when her mum waved her off on a holiday with her father to the Algarve.
Candice's former partner Filipe de Silva (35) failed to return the child at the agreed time.
Police in Faro, Portugal, who are also investigating the Madeleine McCann case, have been tasked with looking for the missing girl.
Candice's husband, Dublin businessman Philip Gannon, said that the family have been going out of their minds with worry.
They were home in Ireland with their two-year-old daughter Olivia over Christmas and have pledged to go back to Portugal to ramp up the search.
"Unfortunately, there have been no new developments recently," Mr Gannon told the Herald.
"Ellie has been missing without trace for over five months now.
"We are submitting a petition to the Portuguese Embassy in London this week and Candice (28) will be on some morning TV shows in London to help raise awareness," he added.
Mr Gannon said that they have appealed to the police in Faro to step up the search as Ellie has been completely prevented from having any contact with her mother, family, friends or school.
"The police have been ordered by the civil courts to look for Ellie but the criminal courts still need to order the police to look for her father," he said.
Ellie was living in Madeira with her mother, stepfather and Olivia, after Ms Gannon won full custody in 2010, following a prolonged court battle.
The family's biggest fear is that Mr de Silva has taken their daughter to Brazil, where he has business interests. Ellie has a British passport because her mother was born in the UK.
Faro police were ordered to look for Ellie on September 13 last but Portuguese police have not issued a warrant for Mr de Silva's arrest for child abduction. The Faro police did not respond to queries from the Herald at the time of going to print.
The court also ordered that Ellie's details should be inserted into the Schengen Information System to help trace her whereabouts.
Mr Gannon said that Mr de Silva's friends and family have all told police that they have not seen him or Ellie since September.
Ms Gannon hopes that through raising awareness, someone will eventually help to reunite her with her daughter.
For more information, go to www.reuniteellie.com.