Why does a higher sampling frequency mess up my bandpass filter?
With an IIR filter, the higher the ratio is of sampling frequency to bandpass filter frequency, the closer the poles are to the complex unit circle in the Z-transform.  Poles close to the unit circle can produce numerical instabilities (ill conditioned computations) when computing the filters response.  This is because any numerical quantization or "rounding errors" can get amplified in the arithmetic recurrences if there is only a tiny difference in location between the pole and the unit circle, even if the pole is "supposed" to be inside.

A better solution is to first downsample the signal before filtering to use an IIR filter that is possibly of a lower order and more stable.  You can upsample back up, if needed, after the filter has been applied.