•Feasible domain analysis for the heliocentric gravitational-wave detection configuration is performed.•A semi-analytical configuration uncertainty propagation method is proposed.•The bounds of the feasible domain are analytically derived. Long-term stability is vital for a space-based gravitational-wave (GW) observatory, which can be affected by orbit insertion errors. To analyze the effects of orbit insertion errors on the configuration stability of a heliocentric GW observatory and find the feasible domain, a semi-analytical configuration uncertainty propagation-based analysis method is proposed in this paper. First, a state transition tensor (STT) technique is employed to propagate the orbit uncertainties of each spacecraft in the configuration. The semi-analytical configuration uncertainty propagation solution is then developed by combining the STT and a Tayler approximation to the stability index uncertainties with respect to the orbit uncertainties. Using an independently and identically distributed assumption, the stable sets at any specified epoch are analytically derived based on the semi-analytical solution. The feasible domain is obtained by intersecting the stable sets at different epochs. Finally, the proposed method is verified and applied to analyze the feasible domain of the Laser Interferometer Space Antenna (LISA) project. Accuracy analysis shows that the relative errors of the proposed semi-analytical configuration uncertainty propagation solution are less than 0.35% for a 10-years propagation. Feasible domain analysis results show that the standard deviations of the position and velocity insertion errors should be less than 45.22 km and 9.05 mm/s, respectively, to guarantee configuration stability. The proposed method could be useful for configuration design and stability analysis of a future heliocentric GW observatory mission.