They have never been very consistent but they have won one election. The proximate cause of their current absence of trust is that they just governed badly. Maybe the consumption tax and the triple disaster were to some extent due to LDP decisions, but the DPJ did really badly in responding to them, and then there were problems that were purely their own fault, like alienating the United States.
They won that election because people were fed up with LDP. You can do that once, but to win again you need to be perceived as trustworthy and that includes an amount of consistency.