The most luminous X-ray sources in nearby elliptical galaxies are likely black hole low-mass X-ray binaries (BHLMXBs). In the Milky Way, such systems are always transient, and with the exception of GRS 1915+105 have burst durations on the order of weeks or months. However, the low duty cycle of short-duration outburst BHLMXBs makes it improbable that any one source would be caught in an outburst during a single snapshot observation. Long-duration outburst BHLMXBs, although much rarer, would be detectable in a series of snapshot observations separated by several years. Our analysis of multi-epoch Chandra observations of the giant elliptical galaxies NGC 1399 and M87 separated by 3.3 and 5.3 yr, respectively, finds that all 37 luminous (>8 x 10(38) erg s(-1)) X-ray sources that were present in the first epoch observations were still in outburst in all of the following observations. Many of these probable long-duration outburst BHLMXBs reside within globular clusters of the galaxies. Conversely, no definitive short-duration outburst BHLMXBs were detected in any of the observations. This places an upper limit on the ratio of short-to-long-duration outbursters that is slightly lower, but consistent with what is seen in the Milky Way. The fact that none of the luminous sources turned off between the first and last epochs places a 95 per cent lower limit of 50 yr on the mean burst duration of the long-duration outburst sources. The most likely scenario for the origin of these sources is that they are long-period (> 30 d) black hole binaries with a red giant donor, much like GRS 1915+105. However, unlike GRS 1915+105, most of the sources show only modest variability from epoch to epoch.