"constantly wary" is correct and usable in written English.
You can use it to describe someone who is always on alert and prepared for possible danger or problems. For example, "The soldiers kept a constant watch on the perimeter, remaining constantly wary of any potential threats."
Moreover, she was constantly wary of what was great in men.
Soon they'd start tumbling about – she was constantly wary of them jumping over the side.
She was alternately called paranoid and prescient, the one who was constantly wary of arrest: for loitering, smoking pot, and hopping turnstiles — the pillars of their daily routines.
The young cast really own this piece and its shows in committed, highly watchable acting, particularly Jasmine Jobson who is outstanding as the constantly wary Latitia.
And she shows the links between him and Mussolini are more blurred then suspected, with D'Annunzio constantly wary of the emerging fascist leader.
The balance between interactivity and narrative thrust is one of the most discussed issues, says Tom Uglow of Google Creative Lab, with the team constantly wary of any interactive element getting in the way of the story.
The civil service that works for these people will constantly be wary and holding back because they don't know whether their leadership is going to be with them in another two weeks.
Humanity is capable of both great achievements and evil deeds, and we must constantly be wary about the latter.
The drivers negotiating and moving that cell-in-the-making must constantly be wary of the drop-off from their garbage pile and the uncontrolled, possibly tumbling sled ride that tipping over the edge could bring about.
"I'm still cautious, I'm still wary, constantly kind of looking over my shoulder," said Duke, the bartender attacked last August.
You sense that Priscilla has always been wary of being the centre of attention, while at the same time being constantly drawn to it.
