Hale T-Pole, a Tongan representative of the Rugby Players and Pacific Players Association, said Vaiomounga's only option would be to extend his Romanian visa, after a previous application for a New Zealand visa was denied.
"We tried everything we could ... when we first heard about it [Vaiomounga's plight] we tried to get him over to New Zealand so it's closer to Tonga and that just didn't work out," T-Pole told the Herald.
"There is a resistance within the New Zealand government against Tongan people that go through this problem."
Vaiomounga's application for an Australian visa was greeted with a similar response last year after he was denied entry due to a combination of his financial and medical circumstances.
T-Pole said he will re-approach the Tongan government during the coming months in a final effort to prompt an agreement in correlation with the New Zealand Ministry of Health and the New Zealand government.
"I will talk to the Tongan government again because we need a long-term solution."
"There's a lot of options, with his visa, I don't think they are going to kick him out of Romania but we want to see what we can do in the long-run because eventually we [will] just keep fundraising and fundraising to keep him there," he said.
Ministry of Health spokesperson Dylan Moran said that if a visa were granted to Vaiomounga on medical terms, treatment would remain at his own expense.
"Treatment options for patients outside New Zealand need to be arranged on a hospital-to-hospital level ... however there would be a cost associated with his care, as he is not a New Zealand citizen," Moran said.
The Ministry of Health's Service's for Pacific Island people Webpage outlines that "Tongan residents must meet eligibility criteria in the same way as any other foreign national in New Zealand".
"A Medical Treatment Committee in the country will consider the medical practitioner's referral ... It does not accept patients whose treatment has commenced prior to approval. Some chronic conditions or conditions requiring ongoing treatment are not covered, and a prognosis of a healthy life for at least five years following treatment is required," the Webpage reads.
With more than 200 people in the Kingdom diagnosed with chronic kidney failure each year and about a third of those in desperate need of dialysis treatment, T-Pole said there's not much more he and Vaiomounga could do but wait.
He told the Herald that the current extensive list of Tongan residents in need of dialysis meant the government could not make any special exceptions or agreements on Vaiomounga's behalf.
"There was this long list and I got confronted with questions like 'we feel so sorry for him but don't understand why we should put him in front of the list when there's still a lot of people in Tonga queuing up for that same help,'" said T-Pole.
Vaiomounga's astonishing story has since prompted the association to educate Pacific Island rugby players on the risks associated with accepting overseas contracts.
"We've got to look in with players going overseas with the agents and the clubs to make sure that there's a lifelong insurance cover for the players to go over."
"It's hard to deal with players from the Islands, any contract they'll take it and we want to put pressure then on the agents to make sure that with all these scenarios if anything happens you're fully covered," he said.
AMAZING love being shown for Sione Vaiomounga...nearly £10K raised in under 24hours! Please continue to dig deep people... let's show the world the #RugbyFamily is alive and strong! https://t.co/zjwQisFWeG
Meanwhile, the JustGiving page which was set up to raise funds for Vaiomounga and his family had raised more than £14,000 (NZD$26,700) by Thursday afternoon.
The money will assist in Vaiomounga's multiple residency applications and the cost of living.