Well, the solution in Digilent_WaveForms_Frequency Sweep Generator and Acquisition (FGEN and MSO).vi is not really what I would call a continuous acquisition, rather repeated or something similar as it has to be restarted all the time which causes gaps in the acquired signal.
What I'm looking for is something like the DAQmx function DAQmx Read.vi which can be used repeatedly without restarting the acquisition, while the sampling is still running.