I think that they can supposedly affect your supply because the breast is not stimulated as effectively by the baby's mouth movements. I could be wrong though. Also the milk pools in the nipple shields so the baby uses a different sucking and swallowing pattern which can potentially cause confusion when presented with a bare breast. I would say that if anyone is bothered by either of these two scenarios, then they are clearly not in enough pain!
Like everyone else on this thread I used nipple shields without any problems, twice in fact. Both times around there is absolutely no way on this earth I could have continued feeding without them.
I can't remember how long I used them for the first time. This time I fed my DD with nipple shields from 2 weeks old to 14 weeks old, so 12 weeks in total. She had an absolute killer suck, my nipples were shredded, she flailed her arms around when I was trying to latch her, frequently grabbing an already agonisingly painful nipple. I was so scared of latching her on I would pull away at the last minute, making matters even worse. I found that nipple shields dulled the pain just enough and provided a physical and psychological barrier. It was definitely worth the undoubted faff.
I think you kind of get to a point where you're more comfortable with feeding and nipple shields start to feel like a hindrance. That's the time when you start thinking about weaning baby off the shields. I say weaning them off, for me both times it was simply a case of taking the plunge and trying without. Within a couple of feeds we had adjusted. It was scary feeding without shields at first, but when you realise the pain is nowhere near as bad as it was you just get on with it.
Of course, I then found that I was experiencing the initial sore nipples at 14 weeks instead of right at the beginning, but that soon resolved itself. With DS it never did work out unfortunately due to an undiagnosed tongue tie. But I am still breastfeeding my 7.5 month old DD - totally thanks to nipple shields!
I really really dislike the bad press that nipple shields get. I didn't try them early enough with DD and as a result she ended up getting a few bottles of formula she wouldn't otherwise have had - I kick myself for that now. If anyone is so desperate they're about to give up, of course they should try anything that might help them - I can't understand how anyone would argue otherwise. I suppose the problem is that if they don't advise against them then women will use them because their nipples are a bit sore, thus running an unnecessary risk of having problems as a result.