The phrase "a thin stretch" is correct and usable in written English.
It can be used to describe a situation or argument that is weak or not well-supported.
Example: "Claiming that the new policy will solve all our problems seems like a thin stretch to me."
Alternatives: "a weak argument" or "a flimsy assertion".
She fell into the business by accident during a thin stretch in the 80's.
The Shatt al Arab is a thin stretch of water that separates Iraq from Iran's southern border.
From Ardara, we took an 12-mile extension to the planned route west to Loughros Point, a thin stretch of land jutting out into an Atlantic bay, where waves rolled for hundreds of yards through shockingly bright blue waters.
There'd be stretches of surfaced roads and often there'd be a cycle path or a pavement and sometimes a thin stretch of something smoother.
As we trailered the horses to Montana's Hi-Line, a thin stretch of country beneath the Canadian border, somewhere in the back of my mind was the concrete fact that once dropped off, our pace would plunge from 65 mph to a steady 4 mph clip.
Not so much a beach as Sahara-on-Sea, Cap Ferret sits at the bottom of the The Lège-Cap Ferret peninsula, a long thin stretch of sand, pine trees and 10 small oyster villages, an hour's drive from Bordeaux.
The lens consists of a thin membrane stretched over a transparent glass window.
Chandler's grins are commonly followed by a cynical chaser about the character's appearance, to make clear that masculine humour is a thin veneer stretched over menace," the academics write.
A thin cloth stretched over the top of the box prevented the insects from escaping and to distribute the sunlight evenly.
Treatment of PSC with AM251 induced a thinner, more stretched shape in the cells, with an increased length but an overall smaller size (Figure 5 C&D).
As we watched the gorillas in the zoo's Great Ape House, Calaya lay on her back atop a thin fire hose stretched high between tree limbs.
