We extend our earlier work, regarding the perturbative stability of string
configurations used for computing the interaction potential of heavy quarks
within the gauge/gravity correspondence, to cover a more general class of
gravity duals. We provide results, mostly based on analytic methods and
corroborated by numerical calculations, which apply to strings in a general
class of backgrounds that encompass boosted, spinning and marginally-deformed
D3-brane backgrounds. For the case of spinning branes we demonstrate in a few
examples that perturbative stability of strings requires strong conditions
complementing those following by thermodynamic stability of the dual field
theories. For marginally-deformed backgrounds, we find that even in the
conformal case stability may require an upper value for the imaginary part of
the deformation parameter, whereas in regions of the Coulomb branch where there
exists linear confinement we find that there exist stable string configurations
for certain ranges of values of this parameter. We finally discuss the case of
open strings with fixed endpoints propagating in Rindler space, which turns out
to have an exact classical-mechanical analog.Comment: 41 pages, 16 figures; v2: minor typos corrected, version to appear in
Nucl. Phys.