I've had sourdough that persisted for a surprisingly long time without molding. Some bread types seem to be more mold-resistant than others.
Something changed with rye bread. It isn't as good as the bread I grew up with. I don't know exactly where the blame goes, but the old rye used to mold in the expected time period; maybe two weeks. The newer rye, aside from way fewer bakers making it, has a different texture; almost spongy, and the flavor isn't as good. My September loaf isn't an anomaly either. That's one reason it lasted so long. Aside from not enjoying it as much as I used to, I left it in the bag in preference of bread that spoils faster, and just didn't get to finishing it in a timely manner.
FWIW, the brand is Pepperidge Farms. They were never my favorite brand, but there aren't many choices for rye anymore. Most bread comes from a couple bakeries anyway. They just stick it in a different bag. I could buy store made rye from Wegmans, but if I'm there, I'd rather have their organic rosemary sourdough bread. Holy shit that stuff's good. I end up eating most of the loaf just sitting at the computer.