Why does my clutch plate burn in a week and fiber found in the stater

Hi @nakulmaharaj

What was checked when the clutch plate was last replaced e.g. was release bearing OK, pressure plate OK, flywheel OK - not warped, clutch cable adjustment OK, clutch hydraulic fluid levels OK, no oil or fluid on the clutch plate etc.?

Could also be due to bad driving habits e.g., riding the clutch on hill starts, revving the engine then slipping the clutch etc.

Here's a link to the service manual for a 2006 RX-8 that may help. Click on Transmission and drivetrain → Clutch to find information re inspecting and replacing the components comprising the clutch assembly and operation procedures.