I don't think it really etches the paint, but does kind of get ingrained in there. I too used to have problems with it. I used to get rid of it with some elbow grease.
First:
1-Get a soaking wet paper towel, let it sit on the spot for a bit(few minutes), then gently wipe away with a microfiber cloth. If there are clumps, let soak longer and breakdown for a clean wipe.
2-Meguiars 3 step wax system. You only need the 1st step(Paint Cleaner/Cleaner formula.
http://www.meguiarsdirect.com/product_detail.do?q=4576
3- Apply the step 1, let dry, remove, reapply as needed it should lift it right out. I used to have leaf stains that washing and cleaning wouldn't take out and this product got rid of them ALL first try. I always, always use Microfiber towels for the most benefit(less harm).
If you want you can do the whole car with the product, get a nice polish then a wax to seal the deal. The 3 step is like 5-8 dollars per step, so at most a $25 deal, but you can use anything you want, ideally just keep the Paint Cleaner around.
Always worked wonders for me.