The Hay Festival has agreed to continue funding part of the library's operating costs following a county council review of 11 branch libraries.
The council said revised budget savings meant it now had until the end of the December to agree the library's future.
One option is to move it into a new school from next January.
A Hay Festival spokesman said it was "alarming" the library faced closure.
"If the 'town of books' is at risk, what hope does anywhere else have? The festival's financial support is a short-term fix for a long-term problem, which we will continue to seek solutions to within our community," he said.
"We all do, however, have a responsibility to our local library. They don't just need money. They need our attention. Our attendance. Our championing."
Hay-on-Wye Library Supporters chairwoman Anita Wright said the next steps were to find a sustainable solution for the library's future.
Community groups and councils have taken over running a number of the county's other libraries, such as Crickhowell which is managed in a partnership with the high school.
The council launched its libraries review last year, saying the authority faced budget savings of Â£29.8m by 2019.
Hay-on-Wye Library in the Powys town made famous for its literature festival has been given a "stay of execution", according to campaigners.