I am watching a friend of DD's a couple times a week after preschool this year. He is 3 yrs. 7 months. He has one of those "blanket with a head attached" loveys.
He is not allowed to hold it at school, but otherwise, he has pretty much free reign of the lovey. . . and he has it all. the. time. He shoves it in his mouth (probably touches the back of his throat. . . seriously) and chews and sucks 100% of the time that he has it. He learned to talk with it in his mouth and I can understand about 1% of what he says (with or without the toy in his mouth). It also smells like_sh!t. The first couple days I watched him I kept thinking he had to go to the bathroom (he is really newly potty trained) so I hounded him all day and then I realized it was the toy. Ew.
I'm really hoping school talks to his parents about the speech issue. . . and I'm just really curious when they decide to put some real limits on the duck.
So what were your limits? My DD is attached to several things, but she never had an oral fixation to them. She sleeps with an army of stuffed animals and has a small, rubber dragon that rides with her in the car and comes along on errands (but not to school).

Ashley Sawtelle Photography
Re: When did you put limits on the lovey?
DS does not put his lovel/blankie in his mouth. so i let him have it all the time. he also bring it to school, but they say he basically leaves it on the floor.
at home, as long as there is 1 in the room, he is ok. but if he is tried, scared or sick he holds it 100% of the time.
Wow, that is tough, especially since it sounds like the parents have not set any boundaries with regards to the lovey. My DS never really got attached to any sort of lovey, so maybe I don't know what I'm talking about, but I'd say by age 2 at the latest, they should be able to separate from the lovey and understand whatever boundaries the parents choose for it (only in bed, only in the car, only at home, or whatever).
In your situation, I think you could absolutely enforce a boundary of your choosing since you are in charge. Particularly since he has it in his mouth all the time, I think you are well justified in not allowing him to have it unless he's taking a nap or having quiet time or whatever. I wouldn't want his saliva dragged all around my house and it doesn't sound like it gets washed often, if ever - yuck!
We have always tried to limit things in the mouth (fingers, toys, blankets, etc.) because of that issue. He did have a pacifier for a long time, but after he turned 2 it was only used at bed/nap time.
L has a blanket and monkey that he takes everywhere. But its more of he just needs to see it there, not that he has to be holding it, etc. If I want to wash either, he is good with it (as long as it isn't right before bed).