Proving current revenue is important, but not the end-all-be-all, what's more important is their path to acquiring revenue-generating customers. They need to prove that their model is sustainable. They also need to prove their churn is not outrageous and that they have a plan to replace the churn that is happening.
Tom conveys " when you say 'accepting the valuation from a start-up' you've got this in reverse. Investors will tell you how the valuation they've assigned to the company and how much money they are willing to invest based on their valuation. You will rarely ever find an investor who takes a startup's own valuation.Business angels are shrewd, experienced, and looking for a 10-20x return and know what your company might be worth of if it succeeds. So, they will value your startup based on that, divided by their 10-20x.
Having a source of revenue and a customer base are added pluses that will likely increase the valuation of the start-up. If the company is not making any money at the present but has a plan to monetise, this is also a plus (take a look at what Twitter is going through right now) but there is no set runway period. It all depends on where the start-up is at in terms of development, users, etc and whether the investor is willing to take on that level of risk.