With 32 sites and open boundaries, for V >> U, it required about 160 sweeps to get 6 decimal places on the energy.
I didn't do any explicit checks on the validity of the state because the energy was reasonable and settled to a definite value (as I said, 6 decimal place accuracy), and the bipartite entropy was reasonable and real-valued. It is possible I missed something, however.
There may be some physical effects at play. With open boundaries, in the CDW phase (V >> U > 0) there are two equivalent ground states that crossover at a domain wall. My calculations took a long time to move the domain wall to the middle of the lattice. You can fix this by pinning the boundaries to enforce one of the two degenerate ground states. There is also the possibility of phase separation/coexistence.
The essence of the difficulty of these effects for DMRG is that the ground state manifold hosts many states with similar energy but very different configuration -- and the different states are hard for the DMRG local-update algorithm to access, at least in the CDW case, because of the low entanglement (low entanglement = few off-diagonal terms in density matrix). Using boundary pinning to artificially select one of the ground states, or a well-chosen initial MPS helps.
I don't have much experience with negative V, although I did do a very limited number of calculations early in my project that came up with strange results, possibly for the reasons above. I didn't go deeper into understanding the reasons at that time, because my project was focused on positive U,V, but also because I had no understanding of what was happening.