The phrase "has remained high" is correct and usable in written English.
You could, for example, use it in a sentence like this: "Unemployment in the region has remained high for the last few years."
Since then, the unemployment rate has remained high.
But the number of migrant deaths has remained high.
Child poverty rates has remained high, at 29% in the same period.
Poverty has remained high for individuals on low incomes without children.
But consumption in the region has remained high, so more containers are coming here.
And you write about how the number of aids cases has remained high among minority women.
Yet the dollar's share of global foreign-exchange reserves has remained high.
Its price has remained high, because it was expensive to develop.
Since 2008 inflation has remained high, despite the RBI's repeated tightening (see chart).
The world's trust in Uncle Sam's ability to pay its debts has remained high.
Despite that, the number of foreign journalists in Washington has remained high.
