tl;dr Because in a DC situation the current is always high so the temperature through the air is always high so the air remains a plasma and remains a good conductor the whole time.
OK I = V/R is how we talk about currents. Current (I) equals the potential (V) over the resistance (R).
An electrical spark is where the potential across an air gap is high enough that the air—normally a good insulator and thus a poor conductor—breaks down into plasma. In that state, the air is hot enough that the electrons that would be bound to the atomic nuclei can flow the way electrons in metal do. This means that the resistance of that air gap goes from being a high number to being a low number.
In the case of a DC spark, we have a constant high potential and with the plasma state a low resistance, so I = V/R = big/small = big current. Since we are putting a high current through a conductor, the temperature of the conductor goes up, and the plasma remains a plasma. It stays a good conductor the whole time.
In the case of an AC spark the AC potential goes from some big positive number of volts, to zero volts, to some big negative number of volts, to zero volts, to some big positive number…you get the idea. At some point I=V/R goes from being big/small to zero/small, which can be long enough for the air to cool off and stop being a plasma and be a bad conductor. So when V is a big (positive or negative) number again in 1/4 of the period of the signal (probably 1/60/4 = 1/240 seconds) the air might be too cool to conduct the current. Then V/R would be Big/HUGE = effectively zero current.
Remember: I'm just some weirdo online. This is not advice. Don't mess around with electricity.