We investigated 201 3He-rich (3He/4He > 0.004 at 0.2-2.0 MeV nucleon-1) solar energetic particle (SEP) events from 1997 September through 2003 December using the Ultra Low Energy Isotope Spectrometer on the A dvanced Composition E xplorer. Both ``impulsive'' (flare-related) and ``gradual'' (CME-related) events are included. The 3He fluences varied only by a factor of 100 above our instrument sensitivity threshold, while the 4He fluences varied by factor of 10,000 above the same threshold. Moreover, there appears to be no significant correlation between the 3He and 4He fluences. We find it striking that with more than 6 years of continuous SEP data, we could not find any SEP event that has 3He fluence higher than 2.0×105 particles (cm2 sr MeV nucleon-1)-1, while the largest 4He fluence observed was 7.0×107 particles (cm2 sr MeV nucleon-1)-1. To the approximation that the event fluence is to first order proportional the number of particles released from the Sun, the observed upper limit for the 3He fluence seems to indicate that only a limited number of 0.2-2 MeV nucleon-1 3He can be released from the Sun in an SEP event.