"consistently remained" is correct and usable in written English.
You can use it when referring to something that has stayed the same over a period of time. For example, "John consistently remained committed to his studies throughout his university years."
Over the years, the food at Lisiano's has consistently remained very good.
In depressed times, when prices for most artists drop, his work has consistently remained recession- proof.
The Philadelphia 76ers have consistently remained atop the list of teams expected to land Leonard.
Here, we have observed that within sleep, NREM sleep consistently remained augmented after the consolidation of cued fear-conditioned memory.
Globally, the number of new HIV/AIDS infections has consistently remained at just over 2 million a year.
In Cambridge cycling has consistently remained a popular means of transport and so investment into cycling has continued over the years.
McDonald's said in a statement: "McDonald's values our employees and has consistently remained committed to them, so in turn they can provide quality service to our customers".
Since their introduction, penile prostheses have consistently remained a superior treatment option for men with erectile dysfunction (ED) refractory to conservative measures.
Only the two largest merchant (that is, open-market) producers, Texas Instruments and Motorola, have consistently remained leaders in the semiconductor industry.
And Ardern has consistently remained New Zealand's preferred leader in the polls since being sworn in, but solutions to some of the nation's problems remain elusive.
"We have consistently remained one of the top-ranked paid news apps since our launch," Greg Clayman, the publisher, said in a statement.
