  In general relativity, the contracted Bianchi identity makes the field
equation compatible with the energy conservation, likewise in $f(R)$ theories
of gravity. We show that this classical phenomenon is not guaranteed in the
symmetric teleparallel theory, and rather generally $f(Q)$ model specific. We
further prove that the energy conservation criterion is equivalent to the
affine connection's field equation of $f(Q)$ theory, and except the
$f(Q)=\alpha Q+\beta$ model, the non-linear $f(Q)$ models do not satisfy the
energy conservation or, equivalently the second field equation in every
spacetime geometry; unless $Q$ itself is a constant. So the problem is
deep-rooted in the theory, several physically motivated examples are provided
in the support.
