Rachel, those leaves could be browning at the tips if you have kept on fertilizing as the weather cooled. The plant grows much slower in cooler weather, so you need to ease back on both feeding and watering in winter. Fertilizer burn typically looks like brown, crispy tips on the leaves. So ramp up the fertilizer in spring, go for max growth with generous fert and water all summer, then ease back as the nights cool in fall.
It's also normal for the oldest leaf to die off first. Evergreen tropicals do this regularly - as they grow more new leaves, the older leaves peter out. Your plant is most likely a division from a much older plant, and that leaf could be several years old. You'll never know.
One more thought on the light situation - if you have an even brighter window for that plant to live in through the winter, your direct sun is so feeble and days so short that I'm sure the plant will do better in as much light as you can give it.
@AnnaZ of course you should divide your monster plant. Clumps of BOP here (in ground) can be as big as Volkswagens. You'll probably have to take a Sawzall to it to cut it into manageable pieces. But I'd leave the divisions pretty big - maybe cut the 20in root ball into 4 pieces? That way you won't have to wait 6 years again for the divisions to bloom. They might sulk for a year or two though.
