Can my employment resignation letter be withdrawn?
Unfortunately, a resignation letter (or, for that matter, resigning or quitting orally, or face-to-face) cannot be withdrawn or taken back unless the employer voluntarily chooses to let you do so. Otherwise, once you resigned, you resigned.
In our lives, there will be many words we cannot take back once they are uttered: saying "I do" at the altar, signing a contract that does not have an early termination clause, pleading guilty in court to some motor vehicle offense…once you do or say these things, you are bound by what you declared. There may be some way down the road to avoid the consequences (e.g., filing an appeal; filing for divorce) but those things tend not to be easy, inexpensive, and/or certain, and do not free you from the immediate consequences of your statement or declaration.
It is the same with resigning from your job. While you may be able to avoid the consequences by re-applying for the position or asking your employer to give you a second chance, that's not the same thing as being able to take back or withdraw the resignation. Keeping your job depends on the free choice of your employer. While they could voluntarily choose to tear up the resignation letter, they do not have to. The resignation is binding when you make it.
Remember: employment in this country is "employment at will." While we usually focus on the employer-side of the equation--that is, on the fact that the employer can terminate an employee at any time, for any reason, without prior warning or notice--there is an employee side to the equation, too. Employees are not forced or compelled to work, but rather can quit or resign at any time, for any reason, without prior notice. The employee's ability to quit at any time means that when he or she does quit, the resignation is effective immediately. Even though it is customary to give "two week’s notice," notice is not mandated or required by the law; it is only custom. So when the employee says "I quit," he or she has quit--the employee has stated that he or she is ending his or her employment and he or she does not have the legal right or opportunity to take it back.
You can always ask the employer to ignore or tear up your resignation, and the employer has the right to do that. But while they have the right, they do not have the obligation. It is 100% voluntary on their part whether to allow you to withdraw your resignation. So by all means ask--but do not count on being able to take back your resignation.
Of course, due to "employment at will," the employer didn't have to wait for you to resign. If they weren't happy with you, they could have terminated you at any time (unless you had a written contract preventing them from doing so). But though your job was not secure even if you had not resigned, there is an important difference between resigning and being terminated. An employee who is terminated, so long as it is not "for cause" (for some wrongdoing, like chronic lateness or excessive absences, violating company policy or ignoring manager instructions, theft or other criminal acts at work, etc.), is eligible for unemployment benefits. But if you resign or quit, you can't get unemployment. A voluntary separation from employment makes you ineligible. Therefore, even if you are unhappy at work, or just had a big row with your manager, think twice--maybe three times--before resigning, since once you do, you cannot take it back and you will not be able to get unemployment benefits. You may be better off in many cases, if there is a problem at work, letting your employer terminate you.