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As the landlord you have the obligation to make the premises livable. After being informed of the problems you have the responsibility to fix them. As long as you fixed them within a reasonable time (varies by state, but is usually 14 days) then the tenant cannot abandon the lease. If you fixed the problems in a reasonable amount of time and made reasonable accommodations, then the lease is still valid, and you can enforce the lease--which could include keeping the deposit, depending on the terms of the lease and what you are out because of the tenant backing out.
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