Have you been keeping up with the maintenance on it? When was the last time the fluid/filter was done to include the converter drain/fill?
Although at this point when symptoms like you are describing appear... probably time for a new trans. Get a new converter while its out. If you do need a new trans, what I would do is find a lower mileage automatic out of a 2004 (2004 only) GT or Mach1. Those were the stronger 4R75w and they are a direct bolt in to all 99-04 cars. Only "gotcha" is that you need to change the OSS sensor pulse count in computer from 6 (4R70w) to 24 (4R75w). Any tuner can do this and a tune is a good thing to get anyway especially with the auto.
2000 Mustang GT Steeda #0048 34k miles. 99 Cobra 4V swapped, FTBR IRS swapped, exhaust, tuned by James Gordon.
Just because I give you advice, doesn't mean I know more than you. Its just means I've done more stupid ****.