A few things could be happening:
1- the aluminum powder compartment is leaking, this could either mean powder is escaping, or that moisture is being allowed to enter.
2- aluminum powder may have escaped during manufacture and over time has coated the inside of the outer screen
3- the peg that makes contact with the inner screen has worn down or is otherwise damaged.
The solution to all three is involves popping the back off of the etch a sketch.
For #1, take off the knobs and carefully pry open the back of the toy. There will be glass glued onto the back, clear it off and super carefully pull the glass sheet off. Dump out the aluminum powder and thoroughly clean everything. Pour a couple tablespoons of new aluminum powder into the back and reseal the glass with hot glue. Put knobs and glue back on and should be good to go.
#2, remove the cover, wipe down, check for seal leaks, fix any you find with hot glue and put back together.
#3, open it up following intructions for #1. Pour aluminum powder into a paper cup, clean everything and then take apart the rods that the knobs move around. They should be able to be popped out, if not, break it, its easy to replace. Get the peg off and check it for damage. If it is broken use epoxy to fix it. Vapor from superglue will ruin the powder over time. If its worn or unrepairable visit a hardware store and look for something similar you can jerryrig in there. Be creative, nobody sees the part just the result. After taking care of it put the powder back, reseal and reassemble. Should be good as new.
I don't know where to get aluminum powder. Try a fireworks manufacturer or craft store, it is quite explosive if exposed to heat so be careful with it. Stuff wants to get everywhere too so watch out for that, getting it off of anything it comes in contact with is near impossible. It will look like little beads, this is because its so fine that any static charge will make it stick to itself, its a powder and if you touch it you will make a mess.