Is there any consumer protection against the manufacturer repeatedly replacing items under warranty until the customer simply gives up?
There are two implied warranties that people should knno about - fitness for a particular purpose and merchantabilty. You are concerned with merchantability. The implied warranty of merchantability basically says that goods are reasonably fit for the general purpose for which they are sold. If something keeps breaking it is not merchantable (generally).
The warranty of merchantability is found in the Uniform Commerical Code and in Texas' Business and Commerce Code. Both at Section 2.314. You can read it, it is not very long, but one important part is, "fit for the ordinary purposes for which such goods are used."
This is an implied warranty, which means it is automatic unless disclaimed. Some states prohibit sellers from disclaiming implied warranties; Texas is not one of them (no surprise there). 2.316 is where we find out how to disclaim the warranty. This is how
to exclude or modify the implied warranty of merchantability or any
part of it the language must mention merchantability and in case of a
writing must be conspicuous
2.316 also says
Language to exclude all implied warranties of fitness is sufficient if
it states, for example, that "There are no warranties which extend
beyond the description on the face hereof."
So a buyer needs to see if the seller and the manufacturer both disclaimed the implied warranties. If so the buyer is going to be limited to the expressed warranties. If they did not disclaim then the remedy is to return the item and get the money back.
So yeah, this is like a lemon law for stuff.
There is a requirement that the seller be a "merchant with respect to goods of that kind." That just means that the buyer didn't buy shoes at a car dealer. That it was the seller's business to sell the thing.
A last note on this. Implied warranties differ from state to state as to who they can be applied against. 2-318 offers three options. Texas chose option 3 - which means that the courts decide if the buck stops at the retailer or if it extends to the manufacturer.
This chapter does not provide whether anyone other than a buyer may
take advantage of an express or implied warranty of quality made to
the buyer or whether the buyer or anyone entitled to take advantage of
a warranty made to the buyer may sue a third party other than the
immediate seller for deficiencies in the quality of the goods. These
matters are left to the courts for their determination.
In other words, unless the implied warranties were disclaimed by both the retailer and the manufacturer, the buyer can go after either for the refund.
And what is cool1 is that a 2013 Texas Supreme Court case found that a buyer of a used engine has a claim against the manufacturer. MAN Engines & Components, Inc. v. Shows. This is different because some states require privity of contract - meaning that only the original buyer can exercise the warranty and they can only exercise against the seller.
EDIT
2.316(c)(2) says
when the buyer before entering into the contract has examined the
goods or the sample or model as fully as he desired or has refused to
examine the goods there is no implied warranty with regard to defects
which an examination ought in the circumstances to have revealed to
him
This basically says that if you know about the defect you waive the implied warranty.
There are two ways to look at this. The first way is that the first defective item is the "the goods or the sample or model" that you have now inspected, so you now know about the defect, and if you buy another you are buying it with defects revealed which waives the warranty.
The other way to look at it is that you do not know that the first one is representative of all the products so it is not until you get the second, or third, that the defect with the goods or the sample or model is representative of all the products, and that it is not until you have this knowledge that the defect is "revealed."
In other words, it depends.
1Cool for consumers, not manufacturers.