I have several clients who are dealing with low performers right now. Many of these issues have been dragging on for months. The managers go through all the predictable stages:
Overlook the low performance.
Verbally point it out and expect it to improve. Offer training.
Document it, threaten to take action, and expect it to improve.
Slowly realize it is never going to improve, but avoid taking the final action of terminating employment.
Stage 4 is where you are really kidding yourself. You are in full out denial - just lying to yourself. Your reasoning becomes muddled as you struggle to avoid the inevitable - you cannot even trust your own judgment anymore. Most of us feel very guilty about firing someone, and have a powerful desire to avoid ugly confrontation. So instead we grasp at all kinds of reasons why maybe it's not their fault - maybe we could have done more to help them. We pounce on any momentary performance improvement or other false signs of hope. We actively, willingly ignore the problem week after week, and unconsciously heap work on the people around the low performer - often doing their work ourselves just to compensate.
Then, when it really becomes unbearable, when it's gone on so long it's embarrassing, then we finally move to stage 5, fire the person and get it over with. You endure one ugly hour in your workweek. Then it's done.
The next day, the sun rises, you breathe in, you breathe out. And gradually you find that all your other employees find a way to come up and say "thank you" for dealing with it. In stage four, you felt like some supervillain - like everyone would hate you for firing the guy. And then, you fire him. A new day dawns and you find out that many of your top people were just worried about you all along - they knew this was harder on you than on the low performer!
Your energy level returns. The team is more cheerful. Productivity soars. And you realize it was not as awful as you built it up to be, and you realize you are really much better off without the low performer dragging everyone down.