One of the pieces of advice that entrepreneurs receive is to ask any investors they meet to introduce them to other investors. This is good advice, but it's incomplete.
You should only ask for introductions to other investors *if* the investor is serious about investing in your deal.
The reason is that experienced investors understand that their reputational capital is just as precious as their financial capital. Entrepreneurs may think that intros are an easy ask, but they're not.
Almost every investor, angel or VC, participates in syndicated rounds. This means that we're repeatedly working with other investors. Because of this, reputational capital is critical. The main way we learn about deals is from other investors. And while we expect to reject nearly every deal someone brings to us (that's just the numbers game of investing), I definitely keep mental tabs on which investors bring me good deals, and which bring me bad ones. Therefore, I know that other investors are doing the same to me.
I guard my reputational capital just like I guard my financial capital, perhaps even more so. This is even more true of VCs, who can obtain more financial capital from limited partners, but have to rely on their own track record for reputational capital.
If I'm not interested in a deal, I might make an intro if pressed, but I'll preface my email to the other investor with a note like, "This deal is outside my sweet spot for the following reasons, but the entrepreneur requested you by name. Do you want to take a meeting."
In other words, I'll help, but not at the cost of my reputational capital. We make these intros because every investor does think differently, and one never knows. But you're a lot better off if an investor makes an intro to help him or her do due diligence or assemble a syndicate, than if an investor makes an intro to get rid of you.