Warranty is not always about the full life of the product. Warranty is completely about the original "contract" in purchase to deal with the time-frame of possible manufacturing defects and their likelihood or relative risk.
My opinion is that a warranty should be held to exactly the length of time that was agreed upon in the original "contract" of the purchase. As soon as there are exceptions, there is too much potential for the exceptions to be taken advantage of.
Now, whether or not the warranty on the Inkbird controller should be longer or not is still a valid question, but it is one that is up to Inkbird to determine and offer in the warranty with their product.
...also, the product "abruptly" ceasing to work is always the case with an electronic product, is it not? It is unlikely that an issue in the circuitry would only make the temperature slightly off from what it should be, since even small failures in a circuit can cause major changes to the logic of the circuit.
The example of "unlimited warranties" is the extreme to prove the point that, as soon as you start to extend the warranty beyond the original agreement, you may start down a slippery slope toward the extreme of "unlimited" warranty. If Inkbird wanted to guarantee the product to the warranty period plus 3 additional months, they would have made the warranty period 3 months longer in order to protect their business with a specific "contract" on the purchase with the warranty.
How long the warranty period should be may be a valid question for Inkbird to continue to assess (obviously not assuming this assessment did not already happen to determine the original number), but a product failing after warranty period and not being covered by the warranty seems completely reasonable to me.
Life of product and manufacturing-defect warranties are two very different things in my mind. Things (especially electronics) fail for many reasons beyond manufacturing defects, so warranty is not necessarily lifetime unless specifically stated. I'm pretty sure that it is absolute fact that all products have some failures just outside of the warranty period. Decision-making requires more information about tendencies and average statistics or risk of failure rate more than just one case on the fringe.
Although it could be bad publicity for a company, there is more to a company image than one situation in which a customer is not satisfied. Though it is disappointing that the temperature probe failed, I think it unfair to claim a company is not standing behind their product when it failed after the warranty period that was agreed upon in the contract of purchase...
I personally hope that anyone reading this would not automatically assume the company is terrible when the information indicates that they upheld their part of the contract. Maybe they will still find it worthwhile to guarantee their product with a longer warranty period or make a temperature probe that is more-easily replaceable in the future? They will make the decision they think best for their company.
I don't know, just my opinions about this situation...