In this paper, test procedures for no fractional cointegration against possible breaks in the persistence structure of a fractional cointegrating relationship are introduced. The tests proposed are based on the supremum of the Hassler and Breitung (2006) test statistic for no cointegration over possible breakpoints in the long-run equilibrium. We show that the new tests correctly standardized converge to the supremum of a chi-squared distribution, and that this convergence is uniform. An in-depth Monte Carlo analysis provides results on the finite sample performance of our tests. We then use the new procedures to investigate whether there was a dissolution of fractional cointegrating relationships between benchmark government bonds of ten EMU countries (Spain, Italy, Portugal, Ireland, Greece, Belgium, Austria, Finland, the Netherlands and France) and Germany with the beginning of the European debt crisis.