He has possibly turned off DNA matching in his profile or deleted his test results.
It isn't uncommon for matches to ignore or not reply to messages, sometimes perhaps because they don't know that they have been sent a message, but some people may not want any contact. They take the test because they want to find out their "ethnicity" and for whatever reason might have very little interest in their ancestry or family tree research.
It's disappointing and can be frustrating, but you have to respect people's right not to engage if they don't want to. If you are lucky with a bit of detective work it is sometimes possible to work out who a match is and research their ancestry yourself in the hope that you find a common link.
Just one other point in case you don't realise. When Ancestry or other companies say "a first cousin match" or any other relationship, it is only a suggestion based on the most probable relationship according to the length of the DNA match that you share. Whilst it may turn out to be correct, there are often several other relationships that can be just as valid, and you can only confirm that a relationship is correct by doing the hard work of paper and records based research to establish the exact link between you.