If we are talking good reputations, then I do not think they will ever win it back. Just like Trade Unions will forever be blamed for the Winter of Disontent, the bankers will forever take the rap for the financial crisis.
Of course in both instances, they were not universally loved to begin with. The Unions had long been an obstacle to progress, and the banks had longtime ripped off companies.
Again, in both instances, the Government(s) were happy for the Unions and banks to take the blame for the mess, to hid their own dismal performance in regulating them.