The mechanism that leads to different fragility values upon approaching the glass transition remains a topic of active discussion. Many researchers are trying to find an answer in the properties of the frozen glassy state. Following this approach, we focus here on a previously proposed relationship between the fragility of glass-formers and their nonergodicity factor, determined by inelastic X-ray scattering (IXS) in the glass. We extend this molecular liquid study to two model polymers— polystyrene (PS) and polyisobutylene (PIB)—for which we change the molecular weight. Polymers offer the opportunity to change the fragility without altering the chemical structure, just by changing the chain length. Thus, we specifically chose PS and PIB because they exhibit opposite dependences of fragility with molecular weight. Our analysis for these two polymers reveals no unique correlation between the fragility and the nonergodicity parameter. Even after a recently suggested correction for a possible contribution of the β relaxation, the correlation is not restored. We discuss possible causes for the failure of the “fragility−nonergodicity factor” correlation, emphasizing the features that are specific to polymers. We speculate that polymers might have specific contributions to fragility related to the chain connectivity that are absent in nonpolymeric systems.