In the file net.cpp function ThreadSocketHandler2() has following lines:

        BOOST_FOREACH(CNode* pnode, vNodes)
        {
             ...
            FD_SET(pnode->hSocket, &fdsetRecv);
              ...
        }

but fdsetRecv size limited (64 items in Windows). So when we have more than 64 connections new connections are successfully accepted, but packets cannot be received from them.
I have tested this situation and confirm:

other peer sends "version" message but the current client dont reply on it if number of connections > 64