The phrase "continue to be busy" is correct and usable in written English.
You can use it when you want to express that a situation is ongoing and has not stopped. For example, "I continue to be busy with work each day."
Both Trump and God continue to be busy.
He will continue to be busy despite the end of his involvement with Morphoses.
Company officials said the expansion reflects their assessment that the mortgage industry from Maine to the Pennsylvania will continue to be busy.
And he will continue to be busy: The fund, which is down 2.7percentt since its start, has investments in five other companies, whose identities it has not yet disclosed.
The submarine graveyards and spent fuel stores, it appears, will continue to be busy.
Partners said offices in Germany and South Korea, for example, have continued to be busy.
He was taken ill last year with diverticulitis but continued to be busy, drawing on a formidable canon of reading including Eric Morecambe's only novel, Mr Lonely, and a dozen stories left by Breece Pancake, a talented American who took his own life in 1979 at the age of 26.
Adrian Greason-Walker, executive director of Wales Tourism Alliance, said camp sites and caravan parks in well-known areas continued to be busy.
The natural resources industry is expected to continue to be a busy spot for takeovers next year as energy demand increases, some bankers said.
Both may continue to be too busy not fighting each other in a matchup that has failed to materialize despite multiple negotiations and an eager public.
A term time visit to any of our library sites will reveal that they continue to be as busy as ever, and the recent opening of the £24m Alan Gilbert Learning Commons, which is now receiving an average of 21,000 visits a week, and has had very little impact on use of the main library (only metres away).
