The observed stratospheric quasi-biennial oscillation (QBO) and the tropospheric Madden-Julian oscillation (MJO) are strongly connected in boreal winter, with stronger MJO activity when lower-stratospheric winds are easterly. However, the current generation of climate models with internally generated representations of the QBO and MJO do not simulate the observed QBO-MJO connection, for reasons that remain unclear. This study builds on prior work exploring the QBO-MJO link in climate models whose stratospheric winds are relaxed toward reanalysis, reducing stratospheric biases in the model and imposing a realistic QBO. A series of ensemble experiments are performed using four state-of-the-art climate models capable of representing the MJO over the period 1980–2015, each with similar nudging in the stratosphere. In these four models, nudging leads to a good representation of QBO wind and temperature signals, however no model simulates the observed QBO-MJO relationship. Biases in MJO vertical structure and cloud-radiative feedbacks are investigated, but no conclusive model bias or mechanism is identified that explains the lack of a QBO-MJO connection.