We demonstrate a novel multilayer polydimethylsiloxane (PDMS) device for selective storage and release of single emulsion droplets. Drops are captured in a microchannel cavity and can be released on-demand through a triggered surface acoustic wave pulse. The surface acoustic wave (SAW) is excited by a tapered interdigital transducer (TIDT) deposited on a piezoelectric lithium niobate (LiNbO3) substrate and inverts the pressure difference across the cavity trap to push a drop out of the trap and back into the main flow channel. Droplet capture and release does not require a flow rate change, flow interruption, flow inversion or valve action and can be achieved in as fast as 20 ms. This allows both on-demand droplet capture for analysis and monitoring over arbitrary time scales, and continuous device operation with a high droplet rate of 620 drops per s. We hence decouple long-term droplet interrogation from other operations on the chip. This will ease integration with other microfluidic droplet operations and functional components.