The day-long, repeating GRB 250702BDE / EP250702a: A unique extragalactic transient

Gamma-ray bursts (GRBs) are singular outbursts of high-energy radiation with durations typically lasting from milliseconds to minutes and, in extreme cases, a few hours. They are attributed to the catastrophic outcomes of stellar-scale events and, as such, are not expected to recur. Here, we present observations of an exceptional GRB\,250702BDE which triggered the {\em Fermi} gamma-ray burst monitor on three occasions over several hours, and which was detected in soft X-rays by the \textit{Einstein Probe} a day before the $\gamma$-ray triggers (EP250702a). We present the discovery of an extremely red infrared counterpart of the event with the VLT, as well as radio observations from MeerKAT. Hubble Space Telescope observations pinpoint the source to a non-nuclear location in a host galaxy with complex morphology, implying GRB 250702BDE is an extragalactic event. The multi-wavelength counterpart is well described with standard afterglow models at a relatively low redshift $z \sim 0.2$, but the prompt emission does not readily fit within the expectations for either collapsar or merger-driven GRBs. Indeed, a striking feature of the multiple prompt outbursts is that the third occurs at an integer multiple of the interval between the first two. Although not conclusive, this could be indicative of periodicity in the progenitor system. We discuss several possible scenarios to explain the exceptional properties of the burst, which suggest that either a very unusual collapsar or the tidal disruption of a white dwarf by an intermediate-mass black hole are plausible explanations for this unprecedented GRB.