This paper considers stability analysis of systems with constantly-proper Callier-Desoer distributed-parameter transfer functions, interconnected via feedback channels with time-varying parameters and bandwidth-limited time-varying delays. A point-wise in frequency condition that implies stability is established by applying a robust stability result based on integral-quadratic-constraints and a linear time-varying generalization of the ν-gap metric. The stability condition is applied in an example to illustrate the proposed analysis method.