What do you mean by "dry patches"? Do you mean the skin is just dry? Sometimes my nipples become a bit dry (especially if I go without a bra), but I wouldn't say I get dry patches. I just use 100% shea butter and it usually takes care of it.
I have gotten dry patches on my nipples, and it's always after my boyfriend has been kissing/sucking on them. I use lotion to help the dryness, and it goes away in a few days.