  Shafieloo ea al. firstly proposed the possibility that the current cosmic
acceleration (CA) is slowing down. However, this is rather counterintuitive
because a slowing down CA cannot be accommodated in most mainstream
cosmological models. In this work, by exploring the evolutionary trajectories
of dark energy equation of state $w(z)$ and deceleration parameter $q(z)$, we
present a comprehensive investigation on the slowing down of CA from both the
theoretical and the observational sides. For the theoretical side, we study the
impact of different $w(z)$ by using six parametrization models, and then
discuss the effects of spatial curvature. For the observational side, we
investigate the effects of different type Ia supernovae (SNe Ia), different
baryon acoustic oscillation (BAO), and different cosmic microwave background
(CMB) data, respectively. We find that (1) The evolution of CA are insensitive
to the specific form of $w(z)$; in contrast, a non-flat Universe more favors a
slowing down CA than a flat Universe. (2) SNLS3 SNe Ia datasets favor a slowing
down CA at 1$\sigma$ confidence level, while JLA SNe Ia samples prefer an
eternal CA; in contrast, the effects of different BAO data are negligible. (3)
Compared with CMB distance prior data, full CMB data more favor a slowing down
CA. (4) Due to the low significance, the slowing down of CA is still a
theoretical possibility that cannot be confirmed by the current observations.
