We report on UV and X-ray observations of the 2024 eruption of the recurrent nova LMCN 1968-12a, a rapidly recurring extragalactic system with a 4.3 year recurrence period and a massive white dwarf (WD). The eruption was discovered on 2024 August 1.8 by , and subsequently monitored using 's UVIT and SXT, along with Swift/UVOT and XRT. The multi-wavelength light curves reveal a rapid UV-optical decline, followed by a plateau phase exhibiting 1.26-day modulations consistent with the orbital period. The Supersoft (SSS) X-ray emission, that emerged by day 5, exhibited a double peak, suggesting variable obscuration that could be due to an inhomogeneous nova ejecta or due to a nova super-remnant along the line of sight. Time-resolved X-ray spectroscopy shows a blackbody component with T K. The SEDs obtained concurrently in the UV, peaking at T 20,000 K and with a source radius 2-3 R, are inconsistent with emission from the secondary star or nova photosphere alone. Instead, the UV emission is attributed to an irradiated accretion disk that survived the eruption. The persistent UV plateau and its temperature suggest that the accretion disk was not completely disrupted and resumed activity within days, consistent with recent findings in other rapidly recurring novae such as U~Sco and M31N~2008-12a.

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