Last night the waiter topped off my iced tea three times and I continued to use the same plastic straw, whereas a single paper straw would not have lasted. It's a wetted time and solubility problem. Paper is water soluble--plastic is not.

I've used bad paper straws that didn't last through a single glass but any I've used in the last year has been much more robust. A better question than paper or plastic would be to ask why your iced tea needed a straw at all.