I never followed up on this issue, but our fix was some combination of these two things. I can't remember if one or both was required to fix our issue:

• Respond may not have liked that we were using a web map with 'layer groups' instead of having all individual asset feature services in the 'root' of the layer list.
  • We moved all asset feature service layers to the root of the layer list in the web map we are using.
• We were using a custom vector tile basemap that was not in WGS1984 projection.
  • We made a modified version of our vector tile basemap to use this projection.
  • This may have been related to this issue, or that might have fixed a different/related issue in the Mobile app.