Considering that we know that each subsequent generation is less righteous than the previous generation — a phenomena known as yeridos ha'doros — how can our generation bring the moshiach if no previous generation could?
According to this article at Chabad.org, based on the teachings of the late Lubavitcher Rebbe zy"a, each generation builds on the achievements of the previous generation. So that even though we may be on a lower spiritual level, we are still furthering the cause of creation and bringing it closer to its ultimate goal. I think that this is similar to the popular idea that each mitzvah we perform adds a brick to the Bayis Shlishi in heaven, which will descend in fire when completed.
In his book Mashiach, Rabbi Immanuel Schochet brings several reasons. See there for more details and sources:
"There is an obvious progression of time which of itself brings us closer to Mashiach and continuously enhances the inherent potential for redemption, in spite of our inferiority."
The fact that this generation is so much worse than the earlier generations is specifically why our actions accomplish more. To quote R' Chaim Vital, “a very small act in this generation is equal to many great mitzvot in others; for in these generations evil is extremely overpowering, to no end, unlike aforetimes!”
All the bad deeds done in previous generations are washed away via atonement, either in this world or the next. They therefore no longer exist. In contrast, Good Deeds last forever and are cumulative. Our good deeds are likened to a midget standing on a giant's shoulders. The midget can see farther than the giant, because he is standing on his shoulders.
The Mabit writes that the idea of a בן (son) comes from the word בנין (structure) because the son builds onto the accomplishments of his ancestors. So we are always adding on to what came before us.
I once heard the following "mashal": A professor took out a bottle, and a pile of rocks, a pile of pebbles, a pile of sand, and a can of beer. He first poured them into the bottle in the order of sand, pebbles, rocks (left out the beer), and they would not fit. He then reversed the order, putting in the rocks, then the pebbles, then the sand, and then poured in the beer. The pebbles filled the gaps between the rocks, and the sand filled the gaps between the pebbles, and the beer soaked into all the crevices and was absorbed. The principle being demonstrated was that if you start from the larger, the smaller will still have room to fit (and there's always room for beer). This is our role - our forefathers made "big" accomplishments, and we are left to "fill in the cracks."
The Chafetz Chaim compares it to the laws of the redemption of fields (Vayikra 25:50), similar to our system of a mortgage redemption, where the price of redemption nearer to the end of the term will be a lot less than earlier on. Similarly, where earlier generations would need huge merits to bring Moshiach earlier, now that we are nearer to the time that he has to come, we can bring him earlier with less merits. You can see it here and here.
I heard many years ago the following. Why do we constantly say "Zecher Lyitziyas Mitzrayim"? The answer was that just like in Mitzrayim when we were in the 49th level of impurity and Chazal say had we sunk any further we would of never been redeemed, so too we pray that even though we are on a lower level then previous generations Hashem should redeem us and Mashiach should come.
Rabbi Shimon Schwab once commented that if he were asked what merit the Jewish people possess that makes them deserving of Moshiach, he would answer:
"...Normally a person who is disappointed over and over again would give up... If we ask what our generation can say for itself as to why it deserves the coming of Moshiach, we reply that we deserve it because: We didn't give up! We waited patiently and we are still waiting - no matter how many disappointments and backslidings we had to experience. We don't know the word yiush, to give up.
The Chofetz Chaim (Tzipisa L'Yeshua, Chapter 1) similarly explains, "With the length of the exile, the merits of the Jewish people grow and become greater from generation to generation from the merits... of their waiting and hoping for the coming of Moshiach for such a long time..."
Your question is a great question.
Let's ask a different question:
How did our redemption Egypt take place?
Rabbeinu Bachayei says that even though the time of the redemption had arrived, they weren’t worthy of being redeemed. However, once they all cried out in unison from the work that they were undergoing, their tefillos were accepted and they were redeemed!
Furthermore, the Medrash states:
“When Israel went out of Egypt, they looked back and saw the Egyptians chasing after them… When Israel saw, they were surrounded on all sides – the sea in front of them blocking their path, their enemy chasing after them, and wild animals on both sides in the desert – they lifted their eyes up to their Father in Heaven, and cried out to the Holy One Blessed be He, as it is written: ‘…and Bnei Yisroel cried out to Hashem.’ Why did Hashem do this to them? Because Hashem yearned for their prayers.”
In fact, the Chofeitz Chayim states something astounding:
“All the many troubles that have fallen upon us, from which we have still not been saved, are because we don’t scream and increase our prayers in response to them. If we had prayed (properly), we would not have returned empty-handed. And it is not enough that (one) prays the Shemoneh Esrei prayer three times each day; several times daily he must pour out his requests in solitude, in his house, from the depths of his heart. The three regular prayers are so routine that one does not really concentrate during them – which is not the case if each person would contemplate in solitude his own plight... then he would pour out his heart like water to Hashem. Such a prayer would emerge with very deep intent with a broken heart and with great humility. Such a prayer will certainly not go unanswered...!”
Rav Yitzchak said, “The salvation of Israel depends only on crying... as it is written: ‘...with crying, they will come, and with lamentations, I will lead them.’”
The Chofeitz Chayim says, "One must demand the redemption, just as with the wages of a hired worker. Failure to do so shows that this matter is clearly not that urgent to us!”
Why do we want the redemption?