Pick slides down strings slightly?

In general, if the strings have been corroded by sweat, it will be harder for anything (your fingers, your pick) to slide down them. You might try a different brand or type of strings. Elixir strings claim to be less affected by sweat. They're evidently coated with something. The coating itself might be a bit stickier than the metal in the strings. They're a bit pricey, but they might be worth a try.