Can spheres leaking charge be assumed to be in equilibrium?

I am struggling with the following problem (Irodov 3.3):

Two small equally charged spheres, each of mass $m$, are suspended from the same point by silk threads of length $l$. The distance between the spheres $x ll l$. Find the rate $frac{dq}{dt}$ with which the charge leaks off each sphere if their approach velocity varies as $v = frac{a}{sqrt{x}}$, where $a$ is a constant.

This is embarrassingly simple; we make an approximation for $x ll l$ and get
$$
frac{1}{4 pi epsilon_0} frac{q^2}{x^2} – frac{mgx}{2l} = m ddot{x}.
$$
We can get $ddot{x}$ from our relation for $v$, so we can solve for $q$ and then find $frac{dq}{dt}$.

However, in general, $frac{dq}{dt}$ will depend on $x$ and hence on $t$. The answer in the back of the book and other solutions around the web have $frac{dq}{dt}$ a constant.

You can get this by assuming that at each moment the spheres are in equilibrium, so that you have $ddot{x} = 0$ in the equation of motion above.

Does the problem tacitly imply we should assume equilibrium and hence $frac{dq}{dt}$ is constant, or am I missing something entirely? I.e. why is the assumption of equilibrium justified? I understand reasoning like “the process happens very gradually, so the acceleration is small compared to other quantities in the problem,” but I don’t understand how that is justified by the problem itself, where we are simply given that the spheres are small (so we can represent them as points) and $x ll l$ (which we have used to approximate the gravity term in the equation of motion).