Edit: I checked and bought these shoes in April 2020. I guess I will try to contact them?!
The product was "Nike Air Zoom Pegasus 36 Trail GTX Gore Tex". I wonder where I should contact them?
I have used Gore-Tex only in shoes, but in various kinds of high-quality shoes (i.e. not cheap), either made by a less known Swiss company, or by brands like Adidas or Asics.
In all cases, I have used daily the shoes for 3 to 4 years until I had to dump them, always due to an excessively worn sole, not because of problems with Gore-Tex.
On the other hand, I think I went through by now about 3-4 pairs of various running/hiking lighter plastic shoes (Merrell, Reichle, Salomon) and in those the membrane is the only thing keeping the water out. Unfortunately, it's generally sewn deep into some plastic mesh, so no way to tell / maintain it even if You'd like to. And one tear in the membrane means that all the water that seeps into the surrounding mesh "will" always find the way into the failed part of the membrane. Unfortunately, the rest of the membrane then tends to still do its part in slowing the moisture on its way out. So it drains / dries much slower than shoes with no membrane.