When does the Post-Newtonian expansion break down? In the book Gravitational waves Vol.1: theory and experiment by M.Maggiore, in chapter 5, page 236, the author discusses the Post-Newtonian (PN) expansion and says that it is valid for small speed and when the gravitational field is not strong.
However, in the note 2 at page 237, the author says that the term small velocity is misleading, since systems with $v\approx c/2$ can be described in the context of PN expansion, one must only include more terms in the $v/c$ expansion. 
So when exactly does the PN expansion break down?
 A: The PN series is asymptotic series, as such and any fixed orbital separation, adding more terms will only improve the approximation so much, and after that adding more terms will possibly only make the approximation worse.
The deeper you get into the strong field regime the worse this gets, leaving less useful PN terms. How many useful terms you get strongly depends on the exact quantity you are looking at. For quasi-circular non-spinning binaries, terms up to 27.5 PN order are known for some quantities (such as the linear in mass-ratio part of the flux). Although the convergence is slow these still seemingly improve the approximation at the last stable orbit.
However for other quantities there seems to be no significant improvement beyond 4PN order. This seems to be particularly the case when you add eccentricity into the picture. For example, take a look at figure 1b in this paper. The EOB q-potential shown here controls the behavior of slightly eccentric binaries. Of the successive PN approximants the 4PN is closest to the exact values calculated using black hole perturbation theory for $u\gtrsim0.1$.  
