Is it true that if a transmission is starting to fail a new transmission fluid will make it worse?

It was (and may still be) a common practice to recommend against fluid changes in an automatic transmission if too many miles had passed without a fluid change. The primary reasons as I understood them were; the new fluid would remove sediment that may have been contributing to the proper function of the transmission, and increase hydraulic pressure, possibly contributing to failure. This practice was especially important in older Fords. I have seen the results first hand.

However, it is possible that the sediment in your transmission is causing problems and a fluid and filter change would improve performance. If you're having problems you only have the cost of a fluid and filter change to loose and the possibility of preventing further damage and failure to gain. Good luck.