  Linear response functions of aging systems are routinely interpreted using
the scaling variable $t_{\rm obs}/t_{\rm w}^\mu$,where $t_{\rm w}$ is the time
at which the field conjugated to the response is turned on or off, and where
$t_{\rm obs}$ is the `observation' time elapsed from the field change. The
response curve obtained for different values of $t_w$ are usually collapsed
using values of $\mu$ slightly below one, a scaling behavior generally known as
\emph{sub-aging}. Recent spin glass Thermoremanent Magnetization experiments
have shown that the value of $\mu$ is strongly affected by the form of the
initial cooling protocol (Rodriguez et al., Phys. Rev. Lett. 91, 037203, 2003),
and even more importantly, (Kenning et al., Phys. Rev. Lett. 97, 057201, 2006)
that the $t_{\rm w}$ dependence of the response curves vanishes altogether in
the limit $t_{\rm obs} \gg t_{\rm w}$. The latter result shows that the widely
used $t_{\rm obs}/t_{\rm w}^\mu$ scaling of linear response data cannot be
generally valid, and casts some doubt on the theoretical significance of the
exponent $\mu$. In this work, a common mechanism is proposed for the origin of
both sub-aging and end of aging behavior in glassy dynamics. The mechanism
combines real and configuration space properties of the state produced by the
initial thermal quench which initiates the aging process.
