IMO, a start-up is characterized by a "double E": Excitement and Equity. All employees of the start-up must be excited because they're doing something new and fun, and something that will make so much money that they'll be able to spend the rest of their lives doing what they please. This latter requires Equity, where all employees will share in the wealth of what they're working so hard to create.
Without both parts of the "double E", there's no incentive to invest the time and energy required: it's just a job. Some companies like to portray themselves as having a "start-up" environment, but too often use this to mean ridiculously long hours doing boring work that will only make a few rich.
It has been my experience that any venture funded startup that doesn't begin to monetize the investment by the end of the third year has failed on their initial plan and are down a modified path either to (a) follow the unexpected turn of events or (b) try to find someway to recover the investment.
Consequently, I think a startup (venture funded) ceases to be a startup when the original business plan has been determined to not be viable. This is of course rarely public knowledge for obvious reasons.
The short answer is when the company actually gets off the ground, makes money and can grow without further investment. By definition, you are a business, though still learning if you are lucky.
Some startups just never make the transition. Predicting the reasons for failure are the issues that Venture Capitalist always assess before they invest.
Smart people are just not enough unless they are backed up with solid financial management, clear goals for success, and a clearly defined market place.
Anything less usually ends in failure.
Just my opinion.
re: "more about financial maturity than it is about how many years have elapsed." For the most part, I tend to agree with this statement. "Start-up" is more of a phase or state of mind than it is a count of days.
However, at some point, it begins to look like the equivalent of an adult still sucking his or her thump. Yes, the company is still in start-up mode, but has been there so long that it just comes off looking immature and ridiculous. When that point hits, is a pretty fuzzy number though.
I'd pick five years as a rough appropriate length of time for a company to call itself a start-up. I would also agree with Betajet that some start-ups use the term long past when they should as an excuse to exploit employees.
What do I think? I think this seems to be what I call a "freewill problem".
People often ask whether we have "freewill". Well, we take in information, store it, process it and act on it. It that fits your arbitary definition of "freewill" then we do have it; if it doesn't, we don't.
Likewise, with this, we seem to have arbitarily come up with a word first and then seem to be debating whether the real world fits our arbitary definition. Why not do it the other way round?
Perhaps we should be talking about "innovative technology start-ups". If I start another bakery, laundry, grocery store, or car dealership, the venture capitalists don't care and my business may putter along for a generation as a privately held company. The characteristic of "innovative technology start-ups" is that they have grand visions to do something new (big enough to interest investors), need capital to build the business, and therefore pass through the various funding stages that merit "start-up" labeling.