A positive example would be an easy proof. It wouldn't find the exact cut-off.
Not that I believe in brute force as an answer to this, and there are still caveats, but I tried the entire range between the end of the 0.5g band and end of the 0.25g band with initial velocities between 4000 and 12000 m/s, and none of them resulted in a single orbit:
![](https://i.imgur.com/oLGccIq.png)
The caveat here is I started all initial velocities +y and position +x (the motion was initially perpendicular to what the force of gravity would have been at the start point).
Please post when you do have a solution, I want to try it out.