  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 GRS1915+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 NGC1399 and M87 separated
by 3.3 and 5.3 yr, respectively, finds that all 37 luminous (>8 x 10^38 ergs/s)
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
GRS1915+105. However, unlike GRS1915+105, most of the sources show only modest
variability from epoch to epoch.
