I assume you're polling the serial port. Fix your code to see what it is doing that stops it from getting back to the UART in time. You as a programmer have to guarantee the minimum service interval for the hardware.
Rewrite your code to use interrupts that receive into a ring buffer.
If you're already using interrupts, watch out for the priority levels. You may need to make the serial port interrupt higher than other interrupts that are taking too long.
Tom
