Dear Mohan,
Basically employment is at will only since it is a contract between two parties. Therefore, the duration of the contract would be a matter of consensus between the parties subject to the provisions of any law in force or general practices in vogue. However, there may arise a situation for the foreclosure of the contract at the option of either party. "Resignation" is the name of the process when the foreclosure is formally initiated by the employee and "discharge simpliciter " when done by the employer. But a certain amount of time is required by the other to make alternative arrangements to avoid the inconvenience caused by the foreclosure decision. It is normally predetermined in the notice clause of the contract.
However, resignation, being only a unilateral move by the employee on his own, if it is effective from a future date, he has the liberty to withdraw it any time before he is relieved just like the employer has the freedom to rescind the order of discharge effective from a future date.
Some times, in consideration of the core activity of the establishment and the importance of the position held by the employee, in public interest as well as in view of the possibility of completion of the alternative arrangement made by the employer, the right to withdraw resignation already submitted by the employee can be restricted with a special clause of approval by the employer. In such a case, once the resignation is formally accepted by the employer, it can be withdrawn only if it is permitted by the employer. Here, I would like to highlight that public interest doesn't cover the interest of the resigning employee but the interest of his/her substitute selected from elsewhere who might be already on the move and in such a situation the employer's refusal to accept the withdrawal of the resignation could be lawful and reasonable as well.
Hence you have to take a decision accordingly.