Autonomous gravitational-wave searches—fully automated analyses of data that run without human intervention or assistance—are desirable for a number of reasons. They are necessary for the rapid identification of gravitational-wave burst candidates, which in turn will allow for follow-up observations by other observatories and the maximum exploitation of their scientific potential. A fully automated analysis would also circumvent the traditional 'by hand' setup and tuning of burst searches that is both labourious and time consuming. We demonstrate a fully automated search with X-Pipeline, a software package for the coherent analysis of data from networks of interferometers for detecting bursts associated with gamma-ray bursts (GRBs) and other astrophysical triggers. We discuss the methods X-Pipeline uses for automated running, including background estimation, efficiency studies, unbiased optimal tuning of search thresholds and prediction of upper limits. These are all done automatically via Monte Carlo with multiple independent data samples and without requiring human intervention. As a demonstration of the power of this approach, we apply X-Pipeline to LIGO data to compute the sensitivity to gravitational-wave emission associated with GRB 031108. We find that X-Pipeline is sensitive to signals approximately a factor of 2 weaker in amplitude than those detectable by the cross-correlation technique used in LIGO searches to date. We conclude with comments on the status of X-Pipeline as a fully autonomous, near-real-time-triggered burst search in the current LSC-Virgo Science Run.