The viral reservoir of the Berlin patient has been examined and it is competent for X4 tropism. The fact that the virus has not re-infected cells (via the CXCR4 receptor) is some combination of factors/luck that we do not understand fully. The leading hypothesis is that the number of X4 tropic infectious particles are simply too low to reseed the replaced immune system.

For background I recommend the original studies of this patient (Hutter 2009, NEJM and Allers 2011, Blood), they contain a wealth of interesting information.