I have the same problem, lines often disappear and when that happens, all I can see in the Graph view are the links floating (new to Obsidian, not sure of the terminology, but words surrounded by double square brackets, some kind of link)… only these link names show in the graph, the lines are all gone, and the circles that usually accompany the note name are also missing.
When this happens, so far the only way I’ve found to fix it is to close Obsidian and re-open it, and even then, sometimes I need to do this close/reopen sequence twice, 'cause sometimes just closing and reopening only once doesn’t resolve the problem, when I close and reopen, sometimes the graph view is still not working and I have to close and reopen a second time (and yes, when I close, I wait 4-7 seconds to make certain the application if completely closed before reopening it again).
Of course it’s behaving now that I would like to take a screenshot, so I’ll take a screenshot later when it acts up again (although, I did update to v0.12.3 earlier today, or late yesterday, so maybe I’ll get lucky and with this new version the problem will be gone).
Windows 7 Ultimate x64
Obsidian v0.12.3