How to approach someone who has stopped replying?
If this is a high-profile researcher, they are likely quite overcommitted and may have indeed legitimately accidentally missed connections.  When dealing with somebody like this, you also need assume that you need to be the one taking the initiative in contact until you've have an established working relationship.

But it also might be that they are uninterested, and either too polite, conflict averse, or culturally trained such that they are unwilling to express their lack of interest directly.

How to tell the difference?  I personally tend to follow the maxim: "Once is happenstance, twice is coincidence, three times is enemy action."  After the third failure to connect (or whatever number you set as your threshold), then it doesn't really matter whether they're flaky or evasive: it's not productive to pursue the connection any further without some sort of positive encouragement from the other side.