Patience is typically required for player performance. If you sign a guy and he struggles, whether you're tweaking something or not, you should give them time to try to work through it. It's easier to cut a guy than replace them. Nobody is going to be the same player for 162 games. Nobody. Obviously the greats are better and quicker at getting back to form, but that's what makes them great. And if you're tweaking a guys motion or swing, it's not reasonable to just cut them loose before that player has a chance to get comfortable with the tweak.
That said, there are definitely instances where this FO has held on too long. They have have solid reasoning to do so, but we don't always know what that is. Pagan is a clear instance of that. Shoemaker and Happ are others, but I'm not sure I would go with a blanket statement that they're unwilling to admit mistakes in general.