How can I retain the talent in the organization during a recession and without a dedicated budget?

This is the heart of the "good talent/employee retention at hard times" .  It comes as a fruit of previous efforts, investments, high corporate culture values and practices,... etc.

Emyloyee loyalty may be difficult to achieve with good talents who realize that they can leave you today and find their new job (employer) next day, and in many times at better pay and better benefits.

This is why I like to stress to my clients (business owners and senior management) that loyalty and commitment is2-way road between them and their employees.   

Overall employee satisfaction taken regularly and reflecting honestly what employees believe and how they view their management, work environment and how they are treated is very very important to build employee loyalty, specially when management takes serious action in light of the results of such surveys.

There are other considerations of course, other views and other tactics that management may turn to ... and it would be premature to try to put everything or assess/judge all these alternatives in such a brief reply to your question. All the best, and if there is anything I can help further with, would be my pleasure !