Sending Messages for Tens of Thousands of Years?

If you send a finite transmission, then that message is going to go past your target in a finite amount of time. The chances that it happens to arrive when somebody is listening do seem pretty small. Do you think our civilization will last long enough to be able to do that? I hope so. If anybody else has made it through, that means we can figure it out too. And i think that's one of the things that to day motivates me to continue working on this project.