In an attempt to fix this issue, I installed GMLive in a new project and copied the files over to the first project. I forgot to remove netlog.exe when doing so. For whatever reason, the issue was fixed. This means that either my installed files were messed up, even though I used the same .gmex file in the new project, or that having netlog.exe in the directory fixed it (even though I am not using Option A).
I must also confess that the issue with the object was my mistake. When I was trying to figure out what was going on with the sprites yesterday, I used GMEdit to add a live call in the object's Create Event, and then wrote "instance_destroy()" below it. After testing to confirm that they did destroy themselves, I removed the line from GMEdit but did not save it, so in GM:S that line still existed. That was my bad :/
If I get this issue again, I will send you a project file with it, but since I can't make it occur again (and really don't want to) I will leave it be for now.