Why is the Split Line at Point tool not splitting at the desired points?

Answer

In some instances, the output created by the Split Line at Point tool does not show the input lines as split at the desired points.There are multiple reasons for this issue, as follows.
 

A Search Radius is not specified

Although the Search Radius parameter is optional, when this is not specified, the tool is designed to split the line based on only the nearest point. Therefore, when multiple points coincide with the line, only one of the points is used to split the line if the Search Radius parameter is not used. Specify the search radius to allow the tool to evaluate each of the points and split the line where it meets the requirements. This expected behavior is shown under Usage in ArcMap Help: Split Line at Point.
 

Using a Polyline feature class

There are some instances of the tool splitting polylines at the desired points and at unwanted vertices of the polylines. This is a known limitation of the software. As a workaround, use the Integrate tool on the line and points before using the Split Line at Point tool, as described below:

1. Make a copy of the data.
2. Run the Integrate tool with the line and point features.
3. Run the Split Line at Point tool with the search radius defined.

Note:
Running the Integrate tool on a copy of the data is important because the tool alters the source data without creating a new output.

The feature class has topology errors

When the line feature class contains topology errors involving gaps and dangles, the Split Line at Point tool does not split lines at the closest point when a Search Radius is not specified. This is because the lines split at the gaps, rather than the desired points. For more information on fixing topology errors, refer to ArcMap Help: Fixing topology errors.
 

A geographic coordinate system is used by the feature class

The tool requires the use of a projected coordinate system to generate accurate results. Use the Project tool to project spatial data from a geographic coordinate system to a projected coordinate system prior to using the Split Line at Point tool.