In the following paper: "On the Cross-Section of Expected Stock Returns: Fama-French Ten Years Later" (by Chou, Chou, and Wang), the authors found, using the Fama-Mac Beth two-pass regression, that the size effect becomes insignificant during the post-1981 period, and the Book/Market effect becomes insignificant during the post-1990 period.
It is important to note that the statistical significance of the Fama-French factors is not only highly sensitive to the sample period used for testing, but also highly dependent on the test assets used as dependent variables. In both Fama-French papers (1993, 2011), the test assets were double-sorted portfolios formed on size and book/market, and/or size and momentum.
The premise of Fama-French seems reasonable: if there are priced factors that are responsible for the size and value premium, then sorting stocks into portfolios based on their size and book/market ratio are likely to result in diversified portfolios that span the factor space.
The problem is that, by grouping all of the assets with similar size or B/M together, any variation in factor loading that is independent of these two firm-characteristics is largely eliminated.
Therefore, in order to have more powerful tests, the LHS(left-hand side) portfolios should be augmented by portfolios with high correlation to the proposed factors, but with imperfect correlation with size and B/M.