In this study, we investigated a poly(ether-block-amide)-5513 (PEBAX-5513)/AgBF4/1-butyl-3-methylimidazolium tetrafluoroborate (BMIMBF4) composite membrane, which is expected to have a high stabilizing effect on the Ag+ ions functioning as olefin carriers in the amide group. Poly(ethylene oxide) (PEO) only consists of ether regions, whereas the PEBAX-5513 copolymer contains both ether and amide regions. However, given the brittle nature of the amide, the penetration of BMIMBF4 remains challenging. The nanoparticles did not stabilize after their formation in the long-term test, thereby resulting in a poor performance compared to previous experiments using PEO as the polymer (selectivity 3; permeance 12.3 GPU). The properties of the functional groups in the polymers were assessed using Fourier transform infrared spectroscopy, scanning electron microscopy, and thermogravimetric analysis, which confirmed that the properties endowed during the production of the film using the ionic liquid can impact the performance.