Problem with Kalanchoe

I received as a gift a Simone Kalanchoe a year ago, and it has done fine, it flowered nicely and has grown quit a bit. I dont water it too much and it gets morning sun, it is a house plant. The leaves look fine. In the summer here in the house the temperature does get into the low 80s about every day, it is dry and hot in the house during the summer.
Suddenly the stem is turning dark brown/black at the base.
I have never fertilized it or re-potted it.
Can someone please tell me what i can do about this, I dont want to lose this plant.
Thank You
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