This paper says brain drain can be a good thing in some cases:

The International Migration of Knowledge Workers: When is Brain Drain Beneficial?, by Peter J. Kuhn and Carol McAusland, WP 12761, NBER, December 2006 [open link]: ABSTRACT We consider the welfare effects of the emigration of workers who produce a public good (knowledge). We ... show that the remaining residents of a country can gain from emigration, even when tastes for knowledge goods exhibit a kind of 'home bias'. ...

1. Introduction. ...[W]e study ...[a] possible source of beneficial brain drain: the direct benefit to sending-country consumers that occurs when its brains move to an environment where they produce higher-quality knowledge goods. More specifically, we model brains as “knowledge workers”, whose efforts improve the quality of a good that is reproducible at zero marginal cost (Rosen 1981).[1] Improvements in the quality of such goods benefit source-country consumers whether their brains live at home or abroad. Thus, for example, scientists sent to a U.S. laboratory, actors sent to Hollywood, and programmers sent to Silicon Valley may produce products of greater value to their origin-country consumers than the products they would have produced at home. Of course, both the amount of home bias in tastes, and the strength of intellectual property rights (IPRs) in the sending and receiving countries will affect the magnitude of these gains in consumer welfare. ...