The makers of Uncle Si's tea paid Si a million dollars for that endorsement. In exchange, they promised that he would be available to help promote the tea. They have not kept that promise, so it is fair that the makers of the tea are suing to enforce the contract.
Product placement is a long standing tradition in TV and Films. Duck Dynasty entered into an arrangement for product placement of Uncle Si's Iced Tea for the show. The makes of Uncle Si's Ice Tea have arbitrarily decided the cast is not drinking enough of it on the show and are threatening a lawsuit. This is the definition of frivolous lawsuit and is a huge waste of tax-payer money.
Was it a part of his contract? This really is important to know, if he signed a contract then it is ok if they do that since he broke it. If not then, no I think that they really should not be able to sure him. So it depends on the situation
I don't think that it's right for the makers of Uncle Si's Iced Tea to sue the drink's namesake for not drinking enough of their iced tea. Even if the product is named after him it doesn't mean it has to be the only thing he drinks, nor does it mean that he has to drink it all the time.