The studies tend to show that VBAC success declines after 40 weeks... but it's not like the success rate falls like a rock or anything! It's a decline in success (and often an increase in the rate of various complications) but it's certainly possible to have a VBAC after 40 weeks. Also it's hard to say how much of the decline in success/increase in risk is due to medical management of a mama who is past her EDD (as defined by modern/western medicine) and how much is biological/physical.

The studies can be found by searching free databases like
PubMed/Medline, and you'll find things like:
Coassolo KM, Stamilio DM, Pare E, Peipert JF, Stevens E, Nelson DB, et al.
Safety and efficacy of vaginal birth after cesarean attempts at or beyond 40 weeks of gestation. Obstet Gynecol 2005;106:700–6.
Quote:
| Women past 40 weeks of gestation were more likely to have a failed VBAC. After controlling for confounders, the increased risk of a failed VBAC beyond 40 weeks remained significant (31.3% compared with 22.2%, odds ratio 1.36, 95% confidence interval 1.24-1.50). The risk of uterine rupture (1.1% compared with 1.0%) or overall morbidity (2.7% compared with 2.1%) was not significantly increased in the women attempting VBAC beyond the EDD. |
and
Landon MB, Leindecker S, Spong CY, et al.
The MFMU Cesarean Registry: factors affecting the success of trial of labor after previous cesarean delivery. Am J Obstet Gynecol. 2005;193(3 Pt 2):1016-1023.
Quote:
| Favorable intrapartum factors included greater cervical dilation at admission for delivery (OR, 2.6; 95% CI, 2.4-2.8, when dilated ≥4 cm), spontaneous labor without need for augmentation or induction (OR, 1.6; 95% CI, 1.5-1.8), and gestational age less than 41 weeks (OR, 1.6; 95% CI, 1.5-1.8) |
and more general articles in industry publications like this:
Predicting the Likelihood of Successful Vaginal Birth After Cesarean Delivery
MARK H. EBELL, MD, MS, Athens Georgia
Am Fam Physician. 2007 Oct 15;76(8):1192-1194.
Quote:
| The review also identified factors that decreased the likelihood of vaginal birth (i.e., more than one previous cesarean delivery; induction of labor; birth weight greater than 4,000 g [8 lb, 13 oz]; and gestational age greater than 40 weeks). |
This article takes info about gestational age from Guise J-M, McDonagh MS, Hashima J, Kraemer DF, Eden KB, Berlin M, et al. Vaginal birth after cesarean (VBAC) volume 1 and volume 2. Rockville, Md.: Agency for Healthcare Research and Quality, March 2003. AHRQ publication no. 03-E018. Accessed July 10, 2007, at: http://www.ncbi.nlm.nih.gov/books/bv...a.chapter.7149.
Anyway...that's the sort of thing that a "well read" OB should have seen. And basically they say yes, success declines. But not by much. The literature doesn't support vbac bans at some predetermined "cut off" gestation! And while some risks increase, the risk of UR doesn't increase significantly.
Good luck and happy birthing! I had two postdate hospital VBACS so I know it can happen!