I think you are not involved in the selection of candidates in the many rounds of interviews. It's one the primary duties in the recruitment process that the selection committee shall submit to the HR a panel of selected candidates in the order of merit. The top ranked one you take it as the successful candidate and send your 'Offer' letter incorporating among other conditions the i) last date to submit/return 'acceptance of your offer' and ii) last date for reporting following receipt of 'acceptance of offer'.
If (i) acceptance of offer is received and the offered candidate willing to join you have to wait till the 'last date for reporting' . If he/she doesn't report by this date or no request for extension of 'joining time' you should take it that this candidate is not going to join. Following this you should initiate action to obtain approval of competent authority to issue alternate offer to the next, the 2nd ranked candidate. Once this is done there is no waiting for 1st ranked one who is declared as 'no show' and he/she should be black listed to apply to any of your vacancies. In the process, if the 1st ranked apply for extension of joining time, you may consider the request on merit or you may decline the extension sought depending on a decision by competent officer(s). This should solve your problem. Therefore it's the step by step process. So ensure the interview committee submit it's 'panel of list of candidates' interviewed which should help you to take appropriate action as I described. I don't feel you should remind or engage in any conversation with a 'candidate not interested' to join. But sometimes the timeline may not be adhered to if the process of BGV and verification of credentials, relieving letter submission in respect of selected candidate gets delayed for some reasons. There is literally nothing, no device to read one's mind. Sometimes the 'interested candidate', really, need not wait till elapse of the 'last date to report' when he/she is free to join with all formalities accomplished.
It is not advisable to call everybody when an 'offered candidate' failed. But should abide by the list of panel in that order. When such things happens there is nothing to worry as I hope, there are plenty of talents still left in India. One suggestion I could make, try 'freshers' who are found to be brilliant, promising and employable. Also try 'campus interviews' for your requirement.
21st February 2019 From India, Bangalore