Should you add more weight to the pendulum bob when the clock doesn't run?

Short answer: no!

Medium answer: adding more weight to the bob increases the per-period energy requirement of the clock, but only up to a limit.  So once you have the clock running reliably, you can (and should) add more weight to the bob to improve its timekeeping stability.

When clock doesn't run because not enough energy is getting refreshed into the pendulum (or other resonator), it's tempting to look for easy fixes.  Adding more weight to the pendulum bob certainly delays the inevitable, since the clock will run longer before stopping.  But it has a certain futile feel to it... will you ever add enough so that it will never stop?  Sadly, you cannot.  Fixing the frictional losses (best) or increasing the drive power are the only solutions.

The reason is a straightforward derivation ending in a simple formula.

First of all, let the angular deflection of the pendulum be A = A(t), a function of time t.  For small angles, this is governed by

A'' + (c/m) A' + (g/L) A = 0,

where m is the pendulum bob mass, g is the acceleration due to gravity, L is the length of the pendulum, and c is the frictional loss constant.  By the usual process for solving such a differential equation, the envelope of the oscillations will naturally decay like

A(t) = exp( - ct/(2m) ) A(0) ( .. trig functions .. ).

If T is the time of one period, the max amplitude is given by

A(T) = exp( -cT/(2m) ) A(0).

Now switching to discuss energy, the height of the pendulum is found by a little geometry...

... to be given by

h = L(1-cos A(t)).

Therefore, the energy change from one period to the next is

dE = mgL(cos(A(T)) - cos(A(0))) = mgL(cos(exp( -cT/(2m) ) A(0)) - cos(A(0)))

again applying a small angle approximation,

This expression is the one we're after, and really we want to know how it changes as we change m.  Clearly at m = 0, the change in energy is zero. Taylor expanding in m, we have the behavior for large m is approximately

Here is a plot of the overall behavior

The takeaway is that as you increase the mass of the pendulum bob, you must supply more energy to sustain oscillations, but only up to a limit.  For stable, reliable operation, you should ensure that the drive supplies at least that limiting amount of energy first first, before increasing bob weight.  Minimizing frictional losses should be the first priority -- which decreases c -- before trying to increase drive weight.  Only after the clock runs reliably should you attempt to increase the pendulum bob weight.