"consistently exhibit" is correct and usable in written English.
You can use it when you want to express that something is done in a way that does not change. For example, "The students consistently exhibit dedication to their studies."
The number of people who consistently exhibit antisemitic attitudes is estimated at anywhere between 10% and 20% in Poland.
They consistently exhibit the intolerance of which they so readily accuse others.
Oligonucleotides modified in this manner consistently exhibit the highest tissue bioavailability (> 90%).
Spatial locations that consistently exhibit large responses are indicative of potential regions of delamination.
Award recipients represent the best of the School's employees, and should consistently exhibit excellent and outstanding work performance.
Award recipients are expected to represent the best of SHASS employees and should consistently exhibit excellent and outstanding work performance.
Design and implement proof assistants that consistently exhibit problem solving behavior considered "intelligent" - in the sense that Deep Blue is an "intelligent" chess player.
But the 2012 model showed all the strengths that Obama and his speechwriters consistently exhibit, producing the best drafts of any president.
Analyses based on landscape position (depression, hilltop, steep slope, and mild slope) showed that locations with mild slopes consistently exhibit time stable features.
Metallic (i.e. zero gap) ionic sulfides consistently exhibit the weakest M S bonds and semi-conductor iono-covalent sulfides the strongest.
Many sociologists, biologists, ethicists, and even economists and management scholars argue that humans consistently exhibit cooperative and altruistic behaviours, which belie an overreliance on the assumption of opportunism found in much economic literature.
