The phrase "constant peril" is correct and usable in written English.
It can be used to describe a situation where someone or something is always in danger or at risk.
Example: "Living in a war zone means that the residents are in constant peril from bombings and violence."
Alternatives: "ongoing danger" or "perpetual threat."
The tempo is in constant peril, of course.
The mistress of a bishop, she's in constant peril of being burned as a witch for her heathen healing methods.
She is credulous and vulnerable and dependent on a protective paternal figure and lives in constant peril of being exploited or corrupted by some lurking cad or villain.
It's madness because tree ferns in pots are in constant peril of drying out, which can set them back a season or kill them outright.
As the ominous plotlines have emerged, the series has morphed into a suspense drama, with Martin and Jake on the run (Season 2 finds them in Los Angeles rather than New York) and in constant peril.
Throughout the museum, the designers seem engaged in curatorial white-water rafting, struggling to keep the displays afloat while in constant peril from the enormous American readiness to be mortally offended by some small misstep of word or tone.
Such constant perils are the biggest selling point at Bernstein's Emerge Logistics.
The Metropolitan Opera was in almost constant financial peril between 1929 and 1944, and there were dicey moments in the 70's.
Servicemen and women, journalists, civilians — anyone out in society — universally agreed that Afghans whose affiliation with the United States was known were in constant mortal peril.
(From the group's Web site: "Fighting the belief that our children are in constant danger from creeps, kidnapping, germs, grades, flashers, frustration, failure, baby snatchers, bugs, bullies, men, sleepovers and/or the perils of a non-organic grape").
That may seem like simple business, but it proves endlessly complex, guided by the constant, shifting perils of global warfare.
