Hi Jason,
The Shrinkwrap can be finnicky.
Try different Wrap Methods and Snap Modes (called Mode with some additional Settings for certain Modes in earlier versions) and check the Normals of both the Source and Target Mesh.
Sometimes, simply Scaling the Source Mesh up a bit, so it encompasses the Target Mesh completely can help.
If you can’t fix it, please post a link to your .blend file, so we can have a look at what’s causing it (and tell us what Blender Version you are using).
