A recent detection of the peculiar neutron star X-ray binary Circinus X-1 with electronic very long baseline interferometry (e-VLBI) prompted the suggestion that compact, non-variable radio emission persists through the entire 16.6-d orbit of the binary system. We present the results of a high angular resolution monitoring campaign conducted with the Australian Long Baseline Array in real-time e-VLBI mode. e-VLBI observations of Circinus X-1 were made on alternate days over a period of 20 d covering the full binary orbit. A compact radio source associated with Circinus X-1 was clearly detected at orbital phases following periastron passage, but no compact radio emission was detected at any other orbital phase, ruling out the presence of a persistent, compact emitting region at our sensitivity levels. The jet was not resolved at any epoch of our 1.4-GHz monitoring campaign, suggesting that the ultrarelativistic flow previously inferred to exist in this source is likely to be dark. We discuss these findings within the context of previous radio monitoring of Circinus X-1.