"consistent access" is correct and usable in written English.
You can use it when you want to refer to a steady or reliable flow of access to something. For example, "The library provides consistent access to books and other resources."
Owning media was the only way to ensure consistent access.
The dealer had shown that he had consistent access to large quantities.
The Affordable Care Act, by contrast, should offer broader, consistent access to care for all women.
Bangladeshi women don't just have access to family planning, they have consistent access.
Without consistent access to the anti-retroviral drugs that have made the disease manageable for many people in the West, Sergeant Leiria has little hope.
Herat has long been a center for burka production, largely because it has a cheap labor and fairly consistent access to electrical power.
Providing a wider safety net and more consistent access to retirement and health benefits will reduce the huge impact of different classifications.
But the promise proved elusive, especially for the underclass who had no consistent access to formal education, even after independence.
After a dose of mindfulness, the default network has greater consistent access to information about our internal states and an enhanced ability to monitor the surrounding environment.
Nearly a third of children in Washington, D.C., the nation's capital, live in homes without "consistent access to food," according to the foundation.
Its most recent data, for 2008, found that 14.6 percent of Americans lacked consistent access to sufficient food, the highest in the survey's 14-year history.
