Hi Tycho,
It sounds like you republished your map service and the layer order has shifted. Please see my response in Dataset Not updating Schema in Collector, this has some troubleshooting suggestions that can help you understand what is happening with your web map.
If you look at the data behind your webmap: http://wasco.maps.arcgis.com/sharing/rest/content/items/31eb6504b48a427ea3392c11124cd85a/data?f=pjso...
You can see how a pop up is created and references an ID in the web map code:
"title":"BaseMap","layers":[{"id":14,"popupInfo":{"title":"School District","fieldInfos"{"fieldName":"OBJECTID","label":"OBJECTID","isEditable":false,"visible":false},
If you republish the service and the layer ID changes, then the popup remains configured pointing to the original layer ID, whereas the data and name may have completely changed.
To address this:
1. Try to not shift layer order when republishing services that exist in built maps (try adding new features at the bottom when possible).
2. Modify your webmap JSON to ensure that the correct layer number is referring to the correct pop up. There are some tools, such as ArcGIS Online Assistant that can help with this.
3. Re-add your map service from rest and reconfigure the pop ups.
Let me know if you have questions.
-Kelly