The assembly from modular parts is an efficient approach for creating new devices in Synthetic Biology. In the "bottom-up" designing strategy, modular parts are characterized in advance, and then mathematical modeling is used to predict the outcome of the final device. A prerequisite for bottom-up design is that the biological parts behave in a modular way when assembled together. We designed a new synthetic device for post-transcriptional regulation of gene expression and tested if the outcome of the device could be described from the features of its components. Modular parts showed unpredictable behavior when assembled in different complex circuits. This prevented a modular description of the device that was possible only under specific conditions. Our findings shed doubts into the feasibility of a pure bottom-up approach in synthetic biology, highlighting the urgency for new strategies for the rational design of synthetic devices.