"has continued to exist" is a grammatically correct and usable phrase in written English.
You can use it when referring to something that has not changed or been eliminated over time. For example: Despite numerous challenges, the ancient Roman civilization has continued to exist in various forms throughout history.
But the N.B.A. has continued to exist quite nicely, meaning the Silnas' haul has been substantial: $255 million and counting.
Indeed, despite the ruling in 2011 that graffiti was no longer a criminal offence, it has continued to exist in a grey area between legal and illegal.
That extracurricular use of my real name means that Wesley Stace has continued to exist on some level over there on the bookshelf.
It is not paradoxical to say that in Italy the monarchy has continued to exist despite the expulsion of the royal House of Savoy, because the monarchical authority of the pontiff has a charisma and a national power of attraction that no president of the republic has ever been able to claim.
After all, it could be argued that solidarity has continued to exist in current welfare states precisely because they have not only implemented multiculturalism and liberal nationalism on the macro level, but have also invested in interculturalism at the meso and micro level.
However, the metropolitan county has continued to exist in law and as a geographic frame of reference, and as a ceremonial county, has a Lord Lieutenant and a High Sheriff.
The road project and its camps had come into existence by his fiat, had continued to exist in fear of his will, and had ended like a blown-out match with his death.
"They've continued to exist for decades without changing very much, because they haven't needed to".
Some of the power that functioned in the unit may have continued to exist, but it was not to be understood any longer as life.
