Theory and observations favor stable helium burning as the most important means to produce fuel for superbursts on neutron star surfaces . However , all known superbursters exhibit unstable burning as well . This ambiguity prompted us to search for superbursts in data from the BeppoSAX Wide Field Cameras of ten luminous LMXBs , most of which do not exhibit normal type-I X-ray bursts . We found no superbursts and determine a lower limit on the recurrence time which varies between 30 and 76 days ( 90 % confidence ) . All recurrence time limits except one are longer than the observed recurrence time for GX 17+2 . This difference can be understood if the mass accretion rate in GX 17+2 is several tens of percent higher than in the other sources ; alternatively , the accreted material in GX~17+2 might be hydrogen deficient , leading to larger carbon yields than in the other sources . We compare our results to the latest models of superbursts . As our search method is indiscriminate of the burst ignition scenario , the recurrence time limits may also be applied to other bursts of similar duration and brightness .