The sefer Tal Oros Vol.1 here explains at length the historical background behind this teaching, but I'll summarize his main points:
Everyone is familiar with the victory of the Maccabeans against the Greeks from the story of Chanukah, but few people know that the fight against the Greeks did not cease at that time, but continued on for several decades. Yehudah the Maccabee fell in battle, as did his brother Yonason after him. But Shimon, the last remaining brother, after another thirty years of fighting finally defeated the Greeks, and for the first time in a very long time Yisrael achieved independence form the Greeks.
But even then the defeated enemy did not give up hope of reclaiming their dominion, and with bribes and trickery they managed to get the brother-in-law of Shimon, Ptolmous ben Chaviv, on their side. He persuaded Shimon to come with some of his family to a family feast, and whilst he was there Ptolmous murdered him. He immediately sent a message to the King of Syria to send an army to recapture Jerusalem, and at the same time sent some people to kill Shimon's son, Yochanan. But Yochanan heard about it, and managed to reach Jerusalem first. (See the Book of the Chasmanoim 67 and the sefer Kadmoniyos by Yosef Flavius, 18,7). By another great miracle they manage to again defeat the enemy, but this time the defeat was total, and the governance of Israel passed into the hands of Yochanan the Chashmonai, and Israel once again became very successful, independent country.
With this background he goes on to explain that from the days of the return to Israel in the time of Ezra they were subservient to different nations, first Persia, then Egypt and then Greece, and had to pay heavy taxes to these kingdoms. Thus they lived in great poverty and distress, and for this reason the last of the prophets instituted that the Levi'im should say Psalm 44 "Wake up, why do You sleep, Hashem?". This prayer was very fitting to their miserable situation at that time, and they were not concerned that people might ask "Does Hashem sleep?", because they all understood that they were saying it as a supplication and a prayer. As the gemara in Sotah 48a says: When Yisrael were living in misery and the nations were living comfortably and in peace, they said "Wake up, why do You sleep, Hashem?".
But during the period of Yochanan the Chashmonai, when Yisrael were "living comfortably and in peace" and their situation was one of prosperity, and thus they no longer agonized about their plight, the words "Wake up, why do You sleep, Hashem?" lost their significance as a prayer and a supplication, and instead caused people to wonder "Does Hashem sleep?". Because of this the decision was taken to annul the reciting of this Psalm by the Levi'im.