Rarely, but occasionally, entrepreneurs will run into the situation described below. It's superficially benign (or better), but is, in fact, tricky, and can have unintended, adverse consequences. Watch your step.
Here's the innocent set-up: a prospective investor whom you've met (Prospective Investor #1) offers to introduce you to another investor they know/recommend (Prospective Investor #2).
What could be better? Clearly a sign of interest by Prospective Investor #1 and -- yes! --a warm introduction to Prospective Investor #2 (see here for the value, even necessity, of a warm introduction).
Here's the catch: unless Prospective Investor #1 has done some serious due diligence and continues to spend time on your deal, there is NO way to have any confidence that Prospective Investor #1 will decide to invest in your company (it is easy for entrepreneurs to mistakenly think that early interest by a VC will lead to an investment; most of the time, indeed, overwhelmingly most of the time, it doesn't).
If Prospective Investor #1 decides not to invest in your company, that is almost always the kiss of death for your chances of success with Prospective Investor #2, even if you haven't met Prospective Investor #2 yet).
Entrepreneurs should know that this is true regardless what the reason given by Prospective Investor #1, even if it is completely unrelated to the evaluation of your company: e.g., "our fund is out of money (yes, my "Sherpa" companies have heard this after several meetings and time-consuming work to respond to investor information requests)", "one of our other portfolio companies unexpectedly objects to our investing in your company", "we've decided that we've done too many deals this year, so we're stopping all investment activities (they will continue to meet with startups, however!)".
So, if Prospective Investor #1 passes, Prospective Investor #2 almost certainly will -- probably without even engaging in any investigation of the opportunity.
There are two main reasons: (1) the "Schmuck" factor and (2) the "Great Deal" factor.
There are different flavors of the Schmuck Factor (see here for another one), but the one that applies here is that no investor gets "blamed" for passing on a hot deal, but they do worry about the "blame" that attaches if another investor they know passes, but they, themselves, go ahead and invest. VC's worry much more about hearing "I told you so!" from another investor than they do in missing out on a great deal (because that isn't tracked as closely, so most often isn't known). And, importantly, it doesn't matter if the deal fails for a reason that was never considered by the investor who passed.
The "Great Deal" factor goes like this: all investors believe that their competitors will do anything to invest in a deal that the competitor believes is a "Great Deal". If the fund is "out of money", they will find money. If another portfolio company objects, they'll figure out a way to invest. If they've done too many deals this year, they'll make an exception for a "Great Deal". So, Prospective Investor #2 will worry enough that Prospective Investor #1 would find a way to invest if Prospective Investor #1 thought your company was a "Great Deal", and that the reason Prospective Investor #1 is offering as to why he's passing is not the real reason. VC's quite often prevaricate when communicationg with their competitors, especially in explaining why they're passing on a deal.
The situaton is entirely different if Prospective Investor #1 has offered a term sheet, or made a similarly credible gesture of their intent to invest. In this situation, their introduction to Prospective Investor #2 is quite helpful.
If they aren't committed, however, entrepreneurs are better off finding another way to get a warm introduction to Prospective Investor #2 (so he won't necessarily know that Prospective Investor #1 has passed), or wait until Prospective Investor #1 has made a commitment to invest.