What is the chance a business owner will lose the time and money invested in a business that proves to be unprofitable?

An unprofitable business, unless supported by owners with deep pockets, will eventually go out of business. When that happens, any time invested in the business and unrecoverable investment would have to be written off so your scenario represents a 100% chance of losing time and money invested. It doesn't have to be that way of course if action is taken to identify areas for a turnaround to profitability before it is too late.