A recent study showed precisely this behaviour. A randomly selected sample of 2500 straight razors were made shave-ready. Each was then shaved with over a period of 3 days under strict laboratory conditions. The razors were then sent to a specially developed stropping laboratory where they were stropped by a purpose-built stropping robot under identical conditions for 200 laps each. During stropping the edge was monitored for shave readiness. The results of the study are best summed up in the following graph taken from Jimbo et al, 2012:
Attachment 110405
It can be clearly seen that approximately 98% shave-readiness is achieved at 60 stropping laps, on average (figures available upon request from corresponding author). Furthermore, increases in shave-readiness are marginal above 60 laps.
The authors conclude that one may strop past the 60 lap mark but that doing so has limited potential to yield a better edge in terms of shave-readiness (p-value < 0.00001).
Reference: Jimbo, G.T., Normous, D. and Biggun, I. V. A. (2012) Interaction Dynamics of High Carbon Steel with Applications to Fast-Stropping Machines in Hilbert Space: Hell Bent on Leather.
Neuture, 69, 221--237.
James.