The CARA should be good for 50,000 ft with a signal validity supplied to the TCAS. If the TCAS is not failing I would think the CARA T/R is working and sending valid signals but the indicators are playing up, possible signal loss! Where is the CARA transmitter/receiver located on your aircraft?
When you switch on does the needle drive to the mask area above the 5000' mark? It takes about 32 seconds for the needle to read zero but there should be no fails RT or LO in this time. the FMCW needs to time in!