Christopher Huxtable, 34, from Swansea, Ken Cresswell, 57, and John Shaw, 61, both from Rotherham, were last week identified as the three trapped men.
Jade Ali, the partner of Mr Huxtable, told reporters: “All these meetings that they’re having, nothing’s coming out of them. We’re just getting kept in the dark.
“It’s just disgusting, we need them out. They’ve given up hope on our men and we’re not going to give up hope.
“We’re going to keep on fighting until they’re home. We are not leaving them there – that’s why we’re here today, to fight to get them out.”
Ms Ali had previously criticised the rescue efforts, saying that her family had been “treated terribly” by authorities since the incident.
She has also set up an online petition to “help the three trapped men in Didcot Power Station” which has been signed by almost 16,000 people.
During the protest, Mr Cresswell’s wife Gail told the BBC: “We’ve got to have them home, we need them home – they need out of this.
“They’re hardworking men who have worked down here all this time and this is the thanks they get, left under rubble all this time.”
The families’ cause received backing over the weekend from Rotherham United FC, with the club offering its support on Twitter .
1/2 #rufc are supporting the campaign to raise awareness of the 3 men who remain trapped following the Didcot Power Station disaster.
— Rotherham United (@OfficialRUFC) March 11, 2016
In a joint statement on Friday, the Health and Safety Executive and Thames Valley Police said: “The priority of the multi-agency response remains the recovery of the missing men so they can be returned to their families. Specialist officers from Thames Valley Police continue to support the families at this difficult time and we are providing them with regular updates on the progress.
“The site owners RWE have overall responsibility for the safety of buildings and structures on their site. They must produce a plan for a safe method of working before the next stage of the recovery can begin. Once this is received and approved by HSE, emergency services are on hand to recover the missing men.
“Preparation at the site, for the recovery, is taking place and will continue over the weekend.
“We are working hard to identify as soon as possible what caused the building to partially collapse, to provide answers and prevent such a tragedy happening again.”
Coleman & Company issued a statement about the missing men last week, saying: “We know how much they are deeply loved and missed by their families. We share their hope that our men are recovered soon and returned home.
Thames Valley Police previously warned it was “highly unlikely” that the three missing men would be found alive.
Part of the 10-storey boiler house at Didcot Power Station collapsed just after 4pm on 23 February.
Michael Collings, 53, from Cleveland, was found dead following the collapse, while five other men were taken to hospital with serious injuries and have since been released.
