in which circumstances can a business survive without profits?

Answer 1

If it is not really a business but is instead a hobby. With a hobby you can do things and be involved but not collect enough money to cover your expenses.

As far as the IRS is concerned if you go 5 years without having a profit in 3 of those years you are not a business (and your "business expenses" are not deductible on your tax filings). You could deduct some expenses under "misc deductions section if they exceed 2% of your income).

Answer 2

If someone is willing to to continue to provide that business with loans, or take an ownership stake for a cash investment.