I'm really not sure, it just sounds like poor digestion to me, and sulfur is a product of anaerobic bacteria, I think. This is gross, but my husband gets a really sulfur-y halitosis if he doesn't do regular tongue cleaning, and that's bacteria fermenting in there. Are there any grain products in her food? Rice or oats? On the occasions I fed grains to my dog (mainly in her old age because she couldn't do as much protein then), they were always long soaked and/or fermented and well cooked to break them down as much as possible, since dogs aren't built to digest grains. Could also be that there are sulfur-based veggies in her food like broccoli or cabbage. I know I don't digest those things very well.
Really, I would look into changing her diet, even if you only do it partially or gradually. Even though she seems healthy now, it won't last if she never gets fresh, raw food. She's deteriorating even though you don't see it, and it will be a lot harder if not impossible to turn her situation around when it's finally manifesting outwardly. All this stuff with dogs getting diabetes and cancer...those are human diseases and the kinds of ailments that afflict kibble-diet dogs when humans interfere with nature, and in my opinion that includes vaccines, though I know these are tough decisions because we want only the best for our pets. My yorkie was like a puppy up until she was about 13 or 14. She had some of the typical toy purebred issues - bad teeth, and eventually cataracts, but her blood work was always good until right near the end when her kidneys went, she never had tumors, diabetes, etc. In retrospect, I don't think we gave her enough variety and I suspect we were short on minerals with her, that's the danger with the home made diets I think, even more than harmful bacterial issues, because it's difficult to prepare really balanced meals on a daily basis, which is why I'm looking at pre-made this time and will probably supplement with vitamins, oils and the tripe, along with some fresh veggies or fruit for snacks, dried liver treats, etc.
Try getting a raw, pre-made dog food, I am looking into this one, but there are others, just google raw diet dogs:
I bet your dog would go nuts for it, finally getting something approximating what nature intended for her. My vet says she thinks every dog is different, and that some dogs can't tolerate raw, but I don't know if I agree. I read so many positive things about even sick dogs improving on raw diets, and I'm seriously going to try the green tripe. My husband won't like that, but it's supposed to be ridiculously healthy for them. The dog I'm adopting this weekend (can't wait!!) has had very poor nutrition all her life so far, we think about 4 years, so part of the damage is done, but I hope to build up her immune system reserves with a super healthy raw diet. She sure deserves it after what she's been through.