I know that my answer is rather late and I like Orangecrush's answer as well. However, I don't think all of the factors of their descent in power has been in their control. To complete the suggestions of Orangecrush's answer, one has to go back a couple of years:
Start & End of the Rafa Benitez Era
Rafa Benitez took over control of LFC at the end of the 03-04 season. He is a tactical mind and has a systematic reign over any club that he chooses to train. I am quite fond of his tactics, especially when it comes to creating deep squads and having a player circulation with the extensive football fixtures out there. After taking control of LFC, he had the infamous AC Milan victory in Istanbul, finished third in the Premier League, became runners-up for the Champions League in 2007 and then followed this all with a 2nd place finish in 08-09. The last year of Rafa's tenure was the following season, when LFC failed and finished 7th in the EPL (source).
Change of Ownership: The Gillet Era
While Rafa Benitez was in control of the football team, Gillet and Hicks became owners of the club to the somewhat dissatisfaction of the loyal Liverpool KOP (Gillet family also own the majority of the Canadiens here in Montreal and that team has not seen any success in decades, either). Only a single season when Rafa Benitez was not successful was enough for the American owners to part ways with him, whereas Rafa's approach (as Arsene Wenger's and Sir Alex Ferguson's) has always been systematic and required patience and stability.
Financial Challenges and loss of Key Players
In 10-11 LFC was very close to bankruptcy and in dire need of cash. The club has already lost key players like Xabi Alonso to the likes of Real Madrid, a key opponent in the European competition. More and more players have parted ways with LFC, while the club struggled to keep hold of even their infamous captain, Steven Gerard. Finally, the club let go of the indispensable Fernando Torres and in a yet undefined, stupid move purchased mediocre players like Andy Carroll.
The coming of the Manchester City FC and Chelsea FC
Last but not least, Manchester City and Chelsea, both regular mid-table performers have been purchased by oil-rich owners and had their bank accounts flooded with money. The teams purchased top talent into the EPL that the likes of which could only competed with Manchester United. With all the money and the following success, it has been very, very difficult for LFC to bring in top talent into the situation.
All the instability caused by the number of departures (especially post-Rafa Benitez era) and the change of power in the EPL have signalled the difficult days ahead for LFC. Arsenal have faced the same situation as well, and are struggling with adapting to the situation. The bringing of Brendan Rogers to lead the team has been a brilliant move, especially after his success at Swansea City. Yet, his challenges are huge; just take a look at the situation created by King Kenny Dalglish and the star forward Luis Suárez.