What exactly does 'reverse use-dependence' mean?
Reverse use dependence is the reduction of a drug's efficacy with the repeated use of the target. This contrasts with ordinary use dependence, for instance with $\mathrm{Na}^+$ blocking local anaesthetics, where they exert more block after tissue use. Reverse use dependence is particularly (but not exclusively) seen with channel blockers such as quinidine.

Quinidine is a $\mathrm{Na}^+/\mathrm{K}^+$ blocker that can slow heart rates, and does so more effectively when the heart rate is already slow. Increased use of the tissue, with a raised heart rate, reduces the effectiveness of the drug. So, strangely, quinidine exerts less block when the target is in use. This is shown in figure 4 from (Breithardt et al., 1995). As the tissue is used less (cardiac cycle length increases), the effect of the drug becomes stronger (action potential duration prolongation increases).


The reverse use dependence of quinidine can be demonstrated on a molecular level with application of quinidine to a voltage-clamped channel with an $\mathrm{i}_\mathrm{Ks}$ current. We see better block when short electrical pulses are given than when longer ones are. The mechanism behind use- and reverse use dependence is by state-dependent affinities, e.g. the drug can bind more easily to the channel in open/closed state. For example, a channel blocker whose binding site becomes occluded when the channel is opened could exhibit use dependent block.

But be warned: reverse use dependent drugs may also exhibit normal use dependence. Quinidine is not just reverse use dependent, but also use dependent 
as a $\mathrm{Na}^+$ blocker. The type of tissue and its state change the effect of the drug and must be taken into account. 

See (Breithardt et al., 1995) for a review of the topic:


  In 1990 Hondeghem and Snyders introduced the concept of reverse use dependence as being a drug effect which is less marked with increased use. Specifically
  quinidine, N-acetyl-procainamide and sotalol lengthened action potential
  duration markedly at slow heart rates but much less or not at all at fast heart rates
  (Fig. 4 [27)). Frequently, reverse use dependence has become equated with reverse 
  use-dependent block of ion channels. Although reverse use-dependent block of ion
  channels can lead to a reverse use-dependent drug effect, this does not need to be
  the case. Worse, reverse use-dependent drug effect does not require reverse use dependent block of channels.


References:


Breithardt, G., Borggrefe, M., Camm, A., Shenasa, M., Haverkamp, W. and Hindricks, G. (1995). Antiarrhythmic Drugs. pp.97-98.