Hmmm, if I were in your shoes, I think the first troubleshooting step would be to create a new project that is not in source control and add the topics to the new project. If they seem to "stick", it would seem to indicate there is something amiss with the source control. If not, there would be something about the topics that needs looking at.
The other test would be to create one single new topic in the project. If it "sticks", again, it would seem to point to something needing to be addressed with the problem topics. File name using odd characters, etc.
I'd suggest re-creating the two topics under entirely new filenames, taking care to avoid non-letters or non-numbers in the filename. Create a note that indicates the new files are substituting for the older topics that were creating problem with source control.
Do you have the setting "Clear project cache (.cpd file) before opening any project" turned on? My stylesheet vanishes whenever I delete the cpd, and on previous projects I've had problems with images vanishing. I have no idea why it happens, but I do have sort of a workaround, although it's messier with source control.
Let me know if you have that setting turned on (or if you delete the cpd file manually) and I'll post back with instructions.
We were able to work around the problem by creating a new topic and and copying the information over to it. Then we deleted the original topics that kept disappearing.
We still have no idea what caused the problem with those two topics in the first place, but at least for now, we think we've solved the problem.
Thanks, everyone, for you help!