I am suspicious about the startup behaviour of U2 (also potentially U1 for the same reason).
In particular ask yourself what happens if U2 output momentarily swings above ground during startup (Which it can do due to the way it is powered), the dynamics are complicated, but I think see a possible instability or latch up.
Try making the positive supply of U2 ground instead of +3V (And the negative supply of U1 ground instead of -3V).
I think there are some words of wisdom in AOE (Second Ed) about this sort of self biasing arrangement and its lockup states.
Regards, Dan.