If you want to get wife to love you again, you have to be familiar with the way female mind works. These lessons you can learn from the psychology of women. A woman does not want to be forced to do what she does want and vice-versa. So, if she wants to leave, then give her your blessings. You can even assist her carry her bags to the car and then wish her well. This will be a great surprise for her because she expects your resistance. She might even start regretting why she did it.
Appearing desperate and pitiful is stupidity. Crying, begging her to come back and even expressing anger are signs of weakness not act of men with a sense of pride. Also never apologize non-stop; if you have been at fault, just doing it once will be enough. If your profuse apology will make her stay, you will not settle the problem permanently. Refrain from bothering her with your calls and messages. In other words, stop all means of communications.
A woman does not want to feel rejected; she wants to have again that thing which she cannot have. If you make her believe that you are out of her life, she would want to get you back. Time is the best healer. How long? It would depend on how serious the damage was. A period of one month is enough time to discover whether your marriage is worth saving or not. It gives you both the opportunity to think things over and act like two reasonable individuals. If you are really meant for each other, then you can both work towards your reconciliation. And happy to say that soon, you get wife to love you again.