According to the Farm Service Agency and Farm Credit, it's difficult to lend to non-profit farms because there is no way to prove that you will have the future cash flow necessary to pay back the debt.
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Most Farm Credit and FSA representatives have not even considered lending to a non-profit institution before so We do not recommend that non-profit farms apply for a loan.

You can call your local FSA or Farm Credit institution to confirm this in your area.

It's possible that there may be some microloans available to non-profit farms through the USDA. Call your local service center to learn more: https://offices.sc.egov.usda.gov/locator/app