Conductivity of Aqueous Ionic Solutions as a Function of Time It is well-known that an aqueous ionic solution can conduct electricity. Let's take the electrolyte NaCl for example. In the diagram below, the circuit consists of a voltage source, a light bulb, and a concentrated NaCl solution. 
Initially, the bulb will shine brightly. Assume the voltage source can source energy forever. My question is: will the NaCl solution allow current to flow forever, or will the conductivity of the NaCl solution degrade over time?

 A: This is really physical chemistry, but since the question is here:
When you electrolyse solutions you need to consider secondary reactions that might take place at the electrodes. For example if you produced sodium at the cathode it would immediately react with water to produce Na$^+$ and hydrogen. Therefore the cathode produces H$_2$ not sodium metal.
Likewise, if the salt solution is dilute the anode produces oxygen. So the net result is that you are splitting the water into hydrogen and oxygen, and as the water is removed over time the concentration of the sodium chloride will get higher and the conductivity of the solution will increase.
However as the concentration of NaCl increases, the reaction at the anode changes and starts producing chlorine instead of oxygen. This produces sodium hydroxide in the cell, which means the concentration of NaCl decreases and the concentration of sodium hydroxide increases. The molar conductivity of NaOH is greater than the molar conductivity of NaCl, so as before the overall conductivity carries on increasing with time.
The solution in the cell will eventually become saturated in sodium hydroxide, but the solubility of NaOH in water is extremely high: from memory it's about 50% by weight. At some point the mobility of the ions is going to start decreasing and the conductivity will fall. However I'm not sure at what point that will happen and whether it happens before or after saturation is reached. Eventually of course the cell will dry out completely and solid NaOH is an insulator.
