Reality check:
Humanity discovers an exoplanet (20 ly) with obvious signs of extraterrestrial intelligence (say there are signatures of large structures made of titan/iridium moving back and forth with speed and pattern which can't be explained by as if they are asteroids, for example)
After some debate, a signal is sent and repeated every day
40, 60, 89 years pass, nothing happens
Question: what is the impact on our hope to find and contact other civilizations?
We've waited long enough, but we still haven't received a reply from them. Could be a lot of reasons for why, but 89 years? Our financiers are getting old and impatient. But on the off chance that they already did yet they remained quiet, what do we do, captain?
They already died? In 89 years, a lot can happen for a civilization that can build megastructures. Nevertheless, we still have to find out why they went silent.
Solution: Send consecutive survey ships. They can generate firsthand knowledge to know what really happened. Instead of having evidence for extraterrestrial life, we found extraterrestrial death and its making us anxious. As for the possibilities of what might have happened, that's a different question.
They're already sending their own survey ships to us? Again, 89 years is a relatively long time. Maybe they prefer actual contact rather than long-distance relationships built on interstellar chat.
Solution: Hope for the best and prepare for the worst, like what we should always do. Raise an army of gentle charming interspecies extroverts but also train them into ruthless killing machines, then arm them to the teeth with bleeding-edge linguistic knowledge and versatile weapons. ET's confirmed, and they've got guts trying to approach us. We're not sure we can meet their standards, and vice versa.
They're already here? Just spying on us before making actual contact, like a real-deal alien stalker.
Solution: Let's go silent instead. This is too dangerous. A stranger we have not yet seen already knows a lot about us. Keep a low interstellar energy emission profile. We found aliens but the search stops now. ET's are paranoid weirdos.
They're not really there? They may not be asteroids or planetoids, but those titan iridium structures are still yet another strange, natural phenomenon that only occurs in space and we know nothing about it.
Solution: Give an award to the person who thought those are signs of intelligent life. He just discovered something entirely new for astronomers. The search for ET goes on, as well as the search for previously-unknown family of celestial bodies.
Nothing really changes. We still do not have concrete evidence of intelligent extraterrestrial life. What we found is our own conjecture of what appears to be the work of what we are actually looking for so let's try to keep looking. Hype more people into getting funds from them, but keep cultivating a sustainable, dependable, wonderful culture so that we'll also be interesting for aliens who might, in return, are also looking for their own aliens.
After some debate, a signal is sent and repeated every day
40, 60, 89 years pass, nothing happens
Because you:
Not to mention... THEY WEREN'T LISTENING!!!
Question: what is the impact on our hope to find and contact other civilizations?
None, because the people who sent the messages knew that these were the most likely outcomes.
They're marching a bunch of war machines around and you expect them to be looking at a couple lights flashing in the sky? That seems like it's unlikely. Instead we should be signalling them daily for the entire 20 years, and then hoping that eventually they'll see it. Probably a bunch of scientists would say something like "they only have a 1/9 chance of seeing our signal so we shouldn't expect a reply for 89 years," and then as soon as people stopped being amazed that we aren't the only life in the universe everyone would just kind of forget in that half way manner, like the way we forget that pipes are basically magic and lightbulbs are freaking amazing.
First of all, since it takes 20 years for light from the rockets to arrive to us and the same amount of time for our signals to get there, they won't be affected for at least 40 years and we won't see a response for at least 40 years after initially sending the signal.
Expecting a response sooner than 40 years would mean expecting they have FTL response methods.
Expecting a response sooner than 20 years would mean expecting they have time travel technology.
Now, here are a few possible scenarios for the 89-year delay (some of which are already mentioned in other answers):
There's really nobody there, and the structures are just an interesting newfound natural phenomenon.
There's nobody there...any more. The structures are all that's left, automatically completing tasks that have been unnecessary for centuries.
There's someone there, but they aren't listening. Perhaps they had their own SETI a few hundred years ago and gave up after a while.
They saw the signal, but refused to respond. Aside from possible cultural and political reasons, interstellar contact is very risky - for what they know, we could be a galactic empire, broadcasting the signal so species living on habitable worlds would give up their location to us. (We should reconsider sending the signal for the same reason - the signal can be traced back to Earth. We've been noisy enough with radio signals already.) Not to mention they could be preparing to invade.
Edit by recommendation: They did respond/are responding, but we're missing/missed it. They may be using a frequency or a form of radiation we can't detect. Or a third, evil alien race may have moved an asteroid into the path of their communication beam. So they're doing their best to reply but we're unable to receive.
What we should do:
