  We study the stability of the many-body scars in spin-1/2 fermionic systems
under the most typical perturbations in relevant materials. We find that some
families of scars are completely insensitive to certain perturbations. In some
other cases they are stable to the first order in perturbation theory. Our
analytical results apply to a large class of Hamiltonians that are known
[arXiv:2106.10300] to support exact many-body scars. For the numerical
calculations we choose the deformed $t-J-U$ model that includes both Heisenberg
and Hubbard interactions. We propose two new stability measures that are based
on physical observables rather than the fidelity to the exact initial
wavefunction. They enable the experimental detection of scars and are more
reliable from the theoretical and numerical perspectives. One of these measures
may potentially find applications in other systems where the exact many-body
scars are equally spaced in energy. In small systems and at small
perturbations, a regime particularly relevant for quantum simulators, we
identify and describe an additional stability exhibited by the many-body scars.
For larger perturbation strengths we observe a distinct mode of ergodicity
breaking that is consistent with many-body localization.
