Thanks for the assist @scottadderton! Nice to see you.
@usconner7796 With "Write clip markers to XMP" enabled, Premiere Pro is going to attempt to actually add marker metadata to your source media files on disk when you add markers to clips in the source monitor. If Premiere Pro determines that it cannot modify the source files of a specific type, it will write siedcare XMP files instead, but if Premiere Pro can modify these source files, it will actually change these source files on disk by inserting this metadata. This is definitely an option/workflow that you want to explicitly enable if you intend to use this feature, and otherwise keep disabled. XMP workflows can be extremely powerful for immediately sharing markers in certain environments, but they do run the risk of creating complications as the source media is altered.
In your case, there could be one of a few things happening. You could have both markers that were saved into your project file (the ones that I'm seeing when I launch your project), and markers saved into the clip XMP data on disk (which I won't see since I don't have your media). So on my side everything looks like it's working correctly when I open your project, but on your side, the clip XMP data is overriding the project XMP data... in which case we are not actually looking at the same set of markers at all. This doesn't totally explain why the marker color is not sticking, even if it is being saved to XMP. We could make some guesses, but I'm not sure that's helpful. That said, it is totally possible that the XMP setting was not enabled for part of your project (which would initially keep markers contained to the project file itself), and then became enabled over the course of the project, creating a workflow branch where XMP markers were now being saved/used in the source media instead of the project.
First, please turn off "Write clip markers to XMP".
Then, please open up a new clip (or import one) that has no markers on it. Try to add markers of different colors. Save, close, and re-open Premiere, and launch that project. See if the marker color now sticks. If it does, this is definitely related to the markers being written down to XMP.
Finally, writing markers to XMP only impacts source media clips. Regardless of the two steps above, you should always be able to add markers of any color to sequences. Please also confirm that sequence markers do hold their color after saving and relaunching Premiere.
The above will confirm whether or not XMP is creating your problem. Unfortunatley, if it is, there's no quick way to convert all XMP markers to Project-centric markers. It'll just be a manual process to fix... or avoid on the next project.