Dear Shomil,
Your current query is related to the grounds/ reasons on which tendered resignation can be accepted and if rejected , consequence thereof.
For first part of your query, please note that the resignation tendered on account of personal exigencies may be generally accepted, if same is requested by placing required advance notice with prescribed time( at least one month if no time frame was conveyed as the term to this effect) or payment of equivalent salary in lieu.
But if the terms of employment / contract provides for that resignation acceptance would be subject exigencies of work / company requirement, then such resignation may not be accepted till alternate arrangements are made.
But in all case owing principle of natural justice , the resignation request has to be acted upon.
Lastly, HR is the face of company management so that is the duty of HR to deal it samrtly.