"continued support for" is grammatically correct and can be used in written English.
Example: Our organization would like to express our gratitude for the continued support for our cause.
I ask your continued support for that.
She offered continued support for our seniors at Tenn South Co-op.
But on Monday, a UN spokesman expressed continued support for the actor.
The poll found continued support for government subsidies for homeownership, including the mortgage interest deduction.
Make no mistake - keeping a lid on oil prices offers continued support for US consumers.
"It's one of the phenomena that explains continued support for the Berlusconi government," he said.
On Monday, she thanked Trump and voiced continued support for his efforts to reduce illegal immigration.
Findings substantiate continued support for the intervention; however, additional resources should include culturally-responsive treatment approaches and academic enrichment programs.
But it was made clear that dropping sanctions was the price of employers' continued support for the entire scheme.
Expanding small business rate reliefs will also go down well as will continued support for key industries.
Following the murder of the US ambassador to Libya, Washington also signalled continued support for the new government in Tripoli.
