haberdashers.
I think you have a case of sunburn at the base. This is often seen when the sun gets lower, and I have to say, also the fact that your pot is not full all the way may cause the reflected heat off the inside of the pot to burn the sides. As long as there is white sap flowing you should be ok. However, it has clearly affected the center section of the plant and caused it to shrivel up and I believe that may be a lost cause at this stage. Your tips still look ok and I would recommend that you cut off the part that looks healthy, and then start cutting down the plant to remove the shriveled part as far as needed until you see the center of the stem white again. Clean your clippers or knife between cuts so you don't spread the rot.
Sorry not to be able to give you better news
