It happens, and it is the outcome that costs us money, so it is worth being clear about. An enquiry can end without an introduction, and none of the ways it does should come as a surprise.
Nobody in the network fits
If the work is outside what our specialists have genuinely delivered, we say so. We will not stretch an agency into a discipline it is learning on your budget, and we will not send you a name simply to have sent one.
An agency is not the right answer yet
Sometimes the problem is a decision the firm has not made rather than a supplier it has not found. When that is what we see, we tell you, even though telling you costs us the introduction. There is a longer version of this on the professional services page.
The fit is close but not close enough
We would rather come back to you in a quarter with the right specialist than introduce an approximate one now. If that is where we land, we will say what would need to change for the answer to be different.
In all three cases you get the reasoning, not a polite decline. That is the part you can use whether or not we are the ones who help.