This may have to do with the way the strings are installed. Someone mentioned ensuring that the ball end spins freely while installing. This is to avoid introducing twist in the string. However, if it's a string through body design, or if the bridge doesn't allow the string to spin freely, then the ball end can't turn while you're stringing up. The key thing here then is to NOT wrap the string around the post - this causes twist in the string which will either unwind or wind more tightly the outer windings of the string around the core, depending on which direction you're wrapping. That's what causes the string to go dead quickly. Instead, run the string through the bridge, establish the witness point over the bridge saddle, measure the desired length needed for winding onto the tuning post, then put a sharp right angle bend in the string at that point (this further prevents unwinding of the wraps). Then cut the string off about 1 1/2 to 2 inches beyond that point (this is the portion that gets shoved down in the hole in the tuning post). Put that portion into the hole in the tuning post, and then wind the string on the post by turning the tuning peg, NOT by wrapping the string around the post. A string winder (either the manual kind or the attachment that goes on an electric screwdriver or drill) will greatly help here, rather than having to manually wind the tuning peg with your fingers all that way.
I used to have that problem with the E and A strings going dead very quickly (or being dead from the start), but once I started changing strings this way the problem went away. Best of luck!