Liquid crystal current flow
LCs materials are dielectric. But they are not perfect insulators and have some non-zero conductivity, allowing a leakage current to flow, slowly discharging the capacitor.
This is caused by mobile ions in the liquid crystal and inside the polyimide layer [2].
Infact a liquid crystal cell can be modeled electrically as this circuit:

               Rl
         _____WWW_____
         |           |
         |     Cl    |
     O--------||---------O


References:
http://www.lintech.org/comp-per/03lcd.pdf‎ p.10-11
http://www.emdmillipore.com/showBrochure?id=200908.037 p.9