The Troubles: Campaigners urge special pension for injured
The centre offers support to anyone traumatised by the conflict in Northern Ireland
The campaigners are known as the "Injured" group.
They have said about 500 people were so badly injured that they were unable to work and could not build up pensions.
Alan McBride from Wave has said they now face having to live on benefits.
"They're now approaching middle age, old age and with welfare reform coming down the line, some of them are facing destitution," he said.
"The campaign is to see something come their way as they approach old age, that they'll be able to live with a bit of independence."
He told BBC NI's Good Morning Ulster that he believed the pension proposal should be "a no-brainer" for politicians and it was a "monumental failure" that a deal had not been agreed.
"There has been a lot of talk recently about money that has gone to groups that are linked to paramilitary organisations and helping them to transition, and we are all for that," he said.
"But what greater transition is there than people who were able-bodied and then, all of a sudden, through no fault of their own were left in the way they have been left?
"The politicians need to step up to the mark."
Paul Gallagher, 44, who was left paralysed after a loyalist paramilitary gun attack in the 1990s, said he was "living a life of pain" with various "physical complications".
'Realisable and affordable'
He said he was frustrated that the pension issue had not been resolved and that it was about "security for the future".
"Most of the people in our group are in their 60s, 70s and 80s, and sadly some members have died waiting on this - we have been at this for five years," he added.
"We have tried to make all the compromises, it is time they (the politicians) made a decision.
"We just can't wait for consensus anymore and for everyone to agree - they just need to make a decision on this to finally get it done."
The campaign has also been backed by the Commissioner for Victims and Survivors, Judith Thompson.
She told Good Morning Ulster that the amount proposed was moderate and achievable.
"People are looking at £4,000 or £5,000 a year per person in addition to benefits. This is not something that is difficult to do."
She said the conditional figure "would be around £2m a year".
It is argued that former paramilitaries may be eligible to get such a pension if their injuries are serious enough.
It is thought 10 former paramilitaries fall into this category. More could come forward if the pension scheme goes ahead.