The phrase 'this incessant' is correct and usable in written English.
It is most commonly used as an adjective that describes something as tedious and unceasing. Example: This incessant rain has been a major nuisance for weeks now.
Why did this incessant intake matter so much to me?
This incessant repetition became the basis of our relationship.
None of this incessant effort brought Burgess much more than transient joy.
"There's this fear, this incessant fear, that guns are bad," she said.
This incessant need to be updated, to receive information on the go that is contained and compact is somewhat unsettling.
I knew that I presented a bit of a problem to them because of all this incessant talking.
It's a call for security-this incessant behavior we have of always wanting to know.
Even round-the-clock cable coverage does not quite convey the drumming repetition of a campaign, and Clinton, for all her weaknesses, is a master of this punishing, incessant rhythm.
To Dunham's eternal credit, she helped to challenge this – her incessant yet casual flaunting of her "imperfect" (translation: normal) naked body (once memorably playing table tennis) was undermining conventional Hollywood ways, where the female form must be slim, perfect and hyper-sexualised, or everyone's eyeballs would spontaneously melt out of their sockets in sheer disgust.
"If you watched the evening news on almost any of the networks, if you read the print media, including the New York Times, there was this constant, incessant emphasis on war with Iraq," Conrad recalled.
Why? Social scientists have a name for this sort of incessant online contact.
