  Pendant drops suspended on the underside of a wet substrate are known to
accumulate fluid form the surrounding thin liquid film, a process that often
results in dripping. The growth of such drops is hastened by their ability to
translate over an otherwise uniform horizontal film. Here we show that this
scenario is surprisingly reversed when the substrate is slightly tilted
($\approx 2$ deg) ; drops become too fast to grow and shrink over the course of
their motion. Combining experiments and numerical simulations, we rationalize
the transition between the conventional growth regime and the previously
unknown decay regime we report. Using an analytical treatment of the
Landau-Levich meniscus that connects the drop to the film, we quantitatively
predict the drop dynamics in the two flow regimes and the value of the critical
inclination angle where the transition between them occurs.
