'been constantly' is a correct and usable part of a sentence in written English, where it is used as an auxiliary verb in the perfect continuous tense.
For example, "She has been constantly working on her project for the past two months."
Dictionary
been constantly
adverb
With steadfastness; with resolve; in loyalty, faithfully.
Exact(60)
It has been constantly exciting to watch.
Most had been constantly hungry.
"My rise has been constantly fighting.
"This whole thing has been constantly moving and shifting".
She had been constantly raped and threatened with death.
The government has been constantly monitoring air, water and food.
The administration insists that it has been constantly engaged.
"We've been constantly busy every day," she said.
Euripides's great anti-war play has been constantly updated.
"They've been constantly on my heels," Mr. Traficant said.
Troops have been constantly on the move since the uprising began.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com