"I've complained because the steaks weren't cooked as well as I would like, and once I waited over an hour for a meal," she told the publication.
"Another time my son's burger was too tough for him to enjoy.
"The staff have always been great and every time they've offered a refund or another meal, it's not something I've ever asked for."
The letter sent to Smith allegedly stated: "We believe as the Coldra, Beefeater are so clearly unable to meet your requirements in terms of the food quality and the level of service provided, that it would be appropriate if you would kindly refrain from visiting the restaurant in future."
The mother of one told the South Wales Argus she had contacted Whitbread, the company that owns the Beefeater chain, after receiving the letter.
She was allegedly told staff had been "keeping tabs on her" after her series of complaints.
A Beefeater spokesperson told the South Wales Argus: "On the past six out of seven visits Miss Smith has complained in order to receive a refund on her meal.
"Our team work very hard to provide all our guests with a welcoming and enjoyable experience; however, it has become evident that we are unable to meet Miss Smith's particular requirements."
Smith said the ban was "outrageous" and that staff should have spoken to her before mailing the letter.
The restaurant has a 3.6-star rating on Facebook and is ranked 78 of 369 restaurants in Newport on TripAdvisor.