The DAQ assistant, while it is great for getting a quick and dirty DAQ task up and running, isn't really designed for high speed data acquisition with precise control. You will likely need to use the lower level DAQmx functions. Start a task, acquire chunks of data in a loop, end the task. You may need to pass the data off to a parallel loop for data processing, display, or logging using a producer/consumer design architecture. Take a look at the DAQmx examples in the example finder.
If you right click on your DAQ assistant and select Open Front Panel, it will turn the Express VI into a subVI that you can open and see how the underlying DAQmx code works.
It may even be a matter of selecting continuous samples in your DAQ assistant, a small number of samples to read, have it in a loop that iterates enough times until you have collected your larger number of samples.