The phrase "a refusal to support" is correct and usable in written English.
You can use it when discussing someone's decision not to provide assistance or backing for a cause, project, or individual.
Example: "The committee's decision was met with disappointment, as it was seen as a refusal to support the community initiative."
Alternatives: "a denial of support" or "an unwillingness to assist".
The student could appeal to the college financial aid administrator for a dependency override, but parent refusal to support the student is not sufficient grounds for an override.
As one of the few Republican critics of the CIA's program, McCain would be the last best hope for getting any aspect of Feinstein's now-token torture legislation through a Senate with a Republican majority -- and his refusal to support it would very likely be the nail in its coffin, at least until the chamber switches parties again.
(The latter statement was in reference to his refusal to support a 2007 immigration bill).
Or take the refusal to support a test-ban treaty; or America's rejection of efforts to add a checking mechanism to the convention banning biological weapons.
Washington clashed with France and Germany over their refusal to support a United Nations resolution authorizing the war, and American officials chided the two nations as representatives of "Old Europe".
David Cameron's refusal to support a new European Union (EU) treaty last December went down well with voters, who rewarded the Conservatives with their first lead over Labour in a year.
In fact, the very principles of tolerance that Stonewall represents are being desecrated by my neighbors' refusal to support a project that promises to improve life in the city as a whole.
As a result of France's refusal to support the American cause in Iraq, freedom fries, and their cousin, freedom toast, replaced French fries and French toast on the menus of some outraged restaurateurs.
Refugee and human rights organisations reacted with anger to the official British refusal to support a sustained European search and rescue operation to prevent further mass migrant drownings, saying it would contribute to more people dying needlessly on Europe's doorstep.
Cuccinelli's refusal to support a mainstream legislative update to Virginia laws reflects his extreme agenda and uncompromising approach".
