The subspace expansion used in the VUMPS code in ITensorInfiniteMPS.jl is a 2-site expansion, and may just fail for certain Hamiltonians (there is a nice explanation of that issue in [2005.06104] Time Dependent Variational Principle with Ancillary Krylov Subspace). This isn’t a limitation of the VUMPS algorithm per se, it is just one subspace expansion approach (specifically, it is the algorithm outlined in Appendix B of [1701.07035] Variational optimization algorithms for uniform matrix product states), is relatively cheap, and which works for many cases.
Something else to try, if the suggestions by @ryanlevy are hard to get working, would be to implement infinite TEBD and do imaginary time evolution (see [quant-ph/0310089] Efficient simulation of one-dimensional quantum many-body systems, [0711.3960] The iTEBD algorithm beyond unitary evolution) for some number of steps before running VUMPS, which will push the system towards the ground state and also entangle it and hopefully circumvent the subspace expansion issues you are seeing, which are likely caused by starting out on a product state. Another option for starting out with a state beyond a product state is to take a product state in the symmetry sector you are interested in and apply a random unitary circuit with infinite TEBD, that kind of state works well as a starting state for finite DMRG so likely would work well for VUMPS as well. Otherwise, you can use infinite DMRG ([0804.2509] Infinite size density matrix renormalization group, revisited) at the beginning of the calculation, which is related to VUMPS but is closer to finite DMRG in that it starts by running DMRG on a small finite system and grows it towards the thermodynamic limit, so if finite DMRG works it may work better for starting out the calculation.
Unfortunately we don’t have infinite TEBD or infinite DMRG implemented in ITensorInfiniteMPS.jl so you will have to implement those yourself.