He made a few mistakes but hardly any more than previous PMs. Burnham doesn't seem to have any grand new plans, it's just business as usual. Three months and his approval is going to be just as bad - if they wanted to ditch the leader they should've done it much closer to an election. It also seems very undemocratic to parachute in a guy who wasn't even an MP to win a safe election so that he could just be handed the leadership with no vote from the parties.
I think this is just going to keep happening as long as the British electorate continue to simultaneously demand massive welfare hikes, more funding for public services and lower taxes all at once. It's just not a rich enough country to afford it all, and it only seems to be stagnating more.