Is this PC in the same subnet as the machines trying to contact it or does the routing between these two subnets forward multicast traffic? If one or the other is not true then I don't think it is multicast causing the issue.
Multicast doesn't connect to a machine anyway. The Multicast receivers subscribe to a multicast session which is handled by the network. The Multicast receivers will send packets now and then to the Multicast session master while the session is going on. But these are generally quite few. This implementation of multicast delivery is designed to not be very chatty when configuring and electing and then waiting. Mostly when the session is being configured agents will register for the session and then just wait until it starts. Every couple of minutes there will be a keep-alive packet sent so that the machines know to keep waiting. So a session should end/timeout within 5 or 10 minutes of the end of the session or something interfering with the keep-alive packets.
Unless there is a huge package being delivered it shouldn't take very long for transmisison to occur. Another thing is that the default speed for multicast is 125 Kbytes/sec which shouldn't generally be much of a network issue.