I have a 1988 RX7 auto, the car runs good up to 65mph and 3500rpms. But once I try to go over 65mph or 4000rpms the car starts sputtering and will not increase
speed. does anyone know what could be causing this and what I can do to correct the problem.

 

Search for 3800 RPM hesitation

 

Sounds to me like your secondary injectors, they should come on around 4000rpm. Check for power to your secondarys and check your injectorys them selfs.