Are the orbits of all triple star systems at least technically unstable? Background:

In the Circular Restricted Three Body Problem (CR3BP, CRTBP) some halo orbits are mathematically stable. That means that the orbit of the third body is closed, periodic, and stable against small perturbations as long as the two primary bodies are in circular orbits around their common center of mass. See answers to Are some Halo Orbits actually Stable?

Question:

But for three massive bodies such as stars, if they are interacting only with each other and only gravitationally, are all orbits still at least technically unstable? 

Yes some systems may last longer than the lifetime of the individual stars, or even the age of the universe, but strictly mathematically are there some stable configurations or are they all mathematically unstable, i.e. one member can eventually be ejected like this?
(Ignoring that all orbits are technically unstable due to the emission of gravitational waves.)

There are known solutions to the gravitational three body problem that can be shown to be stable. Lagrange found a three body solution for general masses where all three orbit the common center of mass in an equilateral triangular formation. Gascheau proved in 1843 that this solution is stable if the component masses satisfy

$$ \frac{m_1 m_2+ m_1 m_3 + m_2 m_3}{(m_1+m_2+m_3)^2} &lt; 1/27$$

More recently, it was shown by Kei Yamada and collaborators (1 2 3) that if one includes the first order Post-Newtonian correction, this solution is modified by a (small) correction to the  triangle legs based on the component masses, i.e. it is only an equilateral triangle if all masses are equal. The general effect of the 1PN interactions is to decrease the region of parameter space where this solution is stable, but for suitably far separated systems there will still be masses for which the system is stable. Moreover, they also proved that (4) these solutions are stable under the emission of gravitational radiation (i.e. a triangular system will adiabatically evolve into another triangular solution).

The effects of 2PN interactions (and beyond) on the stability of these triangular solutions is currently unknown (as far as I am aware).