We develop a self-consistent mean-field extension of deterministic fermionic resetting beyond the quadratic limit. The subsystem single-particle density matrix (SPDM) obeys an exact affine map in the noninteracting repeated-interaction protocol; weak off-site density-density interactions then generate a nonlinear but closed Hartree evolution. We distinguish this deterministic ancillary reset from stochastic quantum resetting and from restart protocols in monitored quantum walks. For the continuous description, the noninteracting affine SPDM equation is induced by a completely positive trace-preserving Gaussian GKLS dynamics. With Hartree feedback the global input-output evolution is nonlinear and therefore is not itself a linear completely positive map; instead, we prove directly that the physical fermionic covariance domain $0\le V\le\id$ is invariant. The proof applies to any Hermitian self-consistent one-body functional, including Hartree-Fock exchange. We also derive a finite-duration reset map that interpolates continuously between no reset and the ideal full reset. Numerical ring calculations explicitly separate stroboscopic resetting from continuous damping and include particle-current and system-environment-coherence observables. Finally, an exact three-site many-body GKLS benchmark quantifies the accuracy of Hartree and Hartree-Fock fixed points and a Jacobian analysis verifies their local stability in the weak-interaction regime.