The Saleae hardware doesn’t have an internal buffer; all of the data while ‘running’ (or ‘playing’) must go to PC software to be processed. As far as I know, you don’t do any triggering in hardware on the device, it is all done in software. So, you must stream it all just to decide when to trigger.
It is not a hardware oscilloscope with any significant device memory buffering, it is a USB logic analyzer that uses PC/host resources to work (buffer, trigger, display).
All that being said, I think you can use the ‘trigger view’ capture mode to get the UI behavior you want.
Note: You may need to use a work-around, depending on exactly how you want it to behave, see:
… and:
Until Saleae implements the feature requested (feel free to ‘up-vote’ it, if you’d like native support for this):