Anne Kelly, from Ashbourne, Co Meath, is housebound and on a list to be vaccinated by the National Ambulance Service (NAS), but her family have been told it has been "inundated" with requests and has hundreds of people to get to.
The HSE said 1,000 housebound patients are yet to be vaccinated.
Mrs Kelly's daughter, Adrienne, has spent the past several weeks trying to get clarity on when her mother will receive her injection.
"I have been trying to get information since March 8," she said.
"Mammy was called for her vaccine on that date, but it's been over two years since she has been able to leave the house, and because she is completely housebound they had to put her on the list for the National Ambulance Service."
After contacting her GP for help, Adrienne was referred to the HSE, which in turn referred her back to the GP.
"This was the loop that went on for days," she said.
"Eventually, I contacted a local TD, Darren O'Rourke. His secretary was contacting the National Ambulance on my behalf and that's when I was told that her name was on a list."
On March 31, Adrienne received an email from the NAS, which explained: "The service in the last while has been inundated with requests from around the country.
"Currently, the service has hundreds upon hundreds of requests to process, and it is only feasible to get to so many in any one day."
Adrienne said her mother became increasingly distraught when news was announced that the roll-out was progressing to younger cohorts.
"It has made Mammy very anxious," she said.
"The reason we are speaking out is because the woman is distraught.
"She watches the briefings every evening and she has been seeing Paul Reid saying, 'We have now completed the over-85s, we have now completed the over-80s'.
"Poor Mammy was absolutely distraught, saying, 'Oh my God, I'm not vaccinated, they have totally forgotten about me, I'm going to fall through the cracks somewhere'.
"She's not sleeping because it's on her mind."
In a statement, the HSE said it cannot comment on individual cases, but "approximately 1,500 people have been ultimately vaccinated in their homes by the National Ambulance Service".
"There are approximately 1,000 people yet to receive their vaccination, but we will get to everyone over the next few weeks," a spokesperson said.
"This is a complex and very vulnerable group, with a significant proportion not available or eligible for vaccination for a number of understandable reasons (already vaccinated, were hospitalised, had transferred to residential care or were too unwell).
"We apologise for the delay, and thank people for their patience as we work together to finish the vaccinations of this group."
Mrs Kelly's daughter said she will continue waiting by the phone.
"At Mammy's age, every day is precious," Adrienne said.
"She said she feels she is being penalised for being housebound, and I think that's appalling.
"She's been living in a complete bubble since last year and you can't take a single day for granted any more.
"We know she isn't the only one, and while we can be a voice for Mammy, there could be people out there who don't have anyone speaking up."