Hi Lindsay,
Modifying the value that your symbology is based off of will result in the symbology changing. If it isn't changing, please share your map so we can take a look as to why the symbology isn't updating.
How many features are in your layer?
If there are less than two thousand, then all of the data is requested in the initial request to the service to improve performance. The application doesn't make a new request for updated data unless the map is refreshed, so its possible if you have only a few features that your aren't seeing the updates due as there is no request for more information.
To confirm this, try making an edit and then refreshing your web map. Does the symbology change? If it does, the above issue is probably what is causing the issue.
To work around this, you can set a refresh interval on the layer: Set refresh interval—ArcGIS Online Help | ArcGIS
this ensures that new data is retrieved from the server depending on the setting. This is really helpful if you are frequently updating the data. If you are updating the data every once in a while, you may be fine to leave the map as is as each time someone navigates to the map, the new data symbology should be shown.
If there are more than 2000 features, the application makes a new request to the server for data each time a user pans and zooms, showing a refresh in the data.
Let me know if this is the issue.
-Kelly