Four or five new outbursts were detected of the bright X-ray transient GRS 1747-312 in the globular cluster Terzan 6 between 1996 and 1999, through monitoring campaigns with the Wide Field Cameras (WFCs) on BeppoSAX and the Proportional Counter Array (PCA) on RossiXTE. This is the first time that the source is seen to exhibit recurrent outbursts after the discovery in September 1990 with ART-P on Granat. Three target-of-opportunity observations in 1998 and 1999, with the narrow-field instruments on BeppoSAX and the PCA, revealed one sharp drop in the flux which we identify as an eclipse of the compact X-ray source by the companion star. A detailed analysis of WFC data identifies further eclipses and we measure the orbital period at 12.360+/-0.009 hr. This is consistent with an identification as a low-mass X-ray binary, as suggested already by the association with a globular cluster. The eclipse duration is 0.72+/-0.06 hr. This implies that the inclination angle is larger than 74°. The 0.1-200 keV unabsorbed peak luminosity is 7*E36 erg s-1. The nature of the compact object is unclear.