Due diligence by an investor, seen from the entrepreneur's point of view, is all good. Really. Here is an opportunity to really learn a lot about your business prospects and gain perspective.
Yes, of course, some investors will use this process to see "how much they can get" and be impolite about it. Fewer than you might think, tho. And my advice is always "walk." Money is only money but business ideas - good ones - are harder to come by.
So think of this as a process of learning - about your venture from a new perspective - about the investor(s) - and about building trust.
The investor is asking if you are trustworthy. If you have the capability to run this venture. If you understand when the venture may need new leadership. (By the way, this issue will always arise. Talk about it in an open way. If the entrepreneur agrees to some sort of leadership strategy it'll probably be in the deal terms.)
She also wants to know if you understand the market dynamics for your proposed business, and if you have thought deeply about eventualities and alternatives. If the entrepreneur is always selling, beyond a certain point this makes investors uncomfortable. If they have been around, they have all seen deals that had hidden facts, or that were interpreted rosily without providing the investor the benefit of the information. Our friends in the VC community, of course, will learn an industry fairly well, and will engage experts as well, so as not to miss something.
It is disarming and refreshing when an entrepreneur explains the risks and the plans to reduce or eliminate them, upfront. The single most important factor for an investor should always be the people and their quality. The basics - integrity, fiduciary responsibility, and so forth - go without saying. Next, I suppose, comes a firm grasp of the facts of the market and the competitive environment. The willingness to be forthcoming and both seek to present the venture and seek investor advice are next.
Each question, each discussion, each exploration always has two purposes. One is the content of the question being discussed; the other is the quality of the entrepreneur in their demeanor and response.
At the same time the entrepreneur has the opportunity to see the investor in action. And to compare the terms and conditions being offered with what the investor has said. If the entrepreneur cannot get an equal sense of a straightforward and fair relationship developing, ask more questions. Have more discussions. If you don't like what you hear, walk. (Of course, make sure you've gotten some third party you do trust to make sure you understand all of the terms before you decide they are unfair!)
If you do see a straightforward and fair relationship evolving, work as hard as you can to build mutual trust. And enjoy the success that will follow.