I absolutely concur with all of the good reasons that have been cited for not accepting “permanent” or “indefinite” loans.
That said, I’ve known several situations that seemed to warrant a bending or breaking of that general rule — where a one-of-a-kind item, central to an institution’s mission, is simply not available as an outright donation or purchase.
If the acceptance of such an item as a permanent/indefinite loan is the only way to “bring it in from the cold,” it may be worth the associated hassles and risks. The “lender” may decide, either within or beyond his/her lifetime, to convert the loan to gift or bequest status. Or, if the institution must eventually deal with the “lenders” heir(s), at least there is evidence of the institution’s interest in the item and the decedant’s interest in seeing the item in the institution’s hands. The institution has a “foot in the door” which may facilitate negotiation with the heir(s) and conversion of the loan to a tax-deductible memorial gift.
The general wisdom, of course, is to regard permanent/indefinite loans as toxic — but there can be exceptions.