Preparing ground states of strongly correlated quantum systems is a central goal in quantum simulation and optimization. The feedback-based quantum algorithm (FALQON) provides an attractive alternative to variational methods with a fully quantum feedback rule, but it fails in the presence of spectral degeneracies, where the feedback signal collapses and the evolution cannot reach the ground state. Using the Fermi-Hubbard model on lattices up to 3x3, we show that this breakdown appears at half-filling on the 2x2 lattice and extends to both half-filled and doped configurations on the 3x3 lattice. We then introduce an imaginary-time-enhanced FALQON ($i$FALQON) scheme, which inserts short imaginary-time evolution steps into the feedback loop. This proposed method suppresses excited-state components, escapes degenerate subspaces, restores monotonic energy descent and improves ground-state convergence across the tested fillings. We further benchmark its performance against existing methods, showing improved results for $i$FALQON, demonstrating the potential of hybrid real-imaginary-time feedback dynamics for ground-state preparation in strongly correlated quantum systems.