This problem was solved on Texas Instruments Forum.
Thanks.
http://e2e.ti.com/support/data_converters/precision_data_converters/f/73/p/627185/2344271#2344271
From the TI forum:
I noticed that you are polling data ready and then performing the data processing/serial output. The serial output operation is likely taking a long time and preventing you from capturing data at the faster data rates. You can try disabling the serial output and using an oscilloscope to see if you're able to reading data at the full throughput; however, when outputting this data over a serial interface you might not be able to capture and display all of the data...
I would try capturing data to memory and outputting the serial data in batches (for example, output 10 samples of data at a time). This might give you a little more data throughput.