If the study on the relationship between W. bancrofti and Wolbachia is correct, then combined with the results of the trials, significant numbers of microfilariae do not survive in circulation beyond what time period

6 months

Explanation:

First, we must remember that doxycline has an effect only on nematodes, but it cannot effectively prevent microfilariae presented before treatment in the blood of the infected. What we can conclude from this is that it is possible that microfilariae grow and develop, however they will not be able to reproduce, since W. bancrofti is completely dependent on Wolbachia for replication. With that, the microfilariae are running out of time and with about 6 months the patients are free of any trace of microfilariae. So we can conclude that 6 months is the longest time that microfilariae survive in circulation.