There is no pause function at the moment. For most of the data settings (especially if you only use low overhead settings like basic telemetry and the ActionScript sampler), the amount of data is very low, so you can run Scout for a long time without running out of memory (I've run Scout profiling content continuously for more than a day, with it using only about a gigabyte of memory).
For the high overhead settings, memory is more of a problem. For Stage3D, you can start it in "delayed" mode (choose from the dropdown - "immediate" is the default). This still captures all the Stage3D commands, but doesn't load them into memory until you click "start recording" in the Stage3D Rendering panel. When it does, it constructs a condensed version of the earlier commands, so you can still replay subsequent frames (it has all your textures, etc), but without using as much memory. You can only do this once though - there's no way currently to start and stop Stage3D recording.