Dear Gazal,
There are two issues about this probationer. One is his dire need for a job, and the other is his sense of responsibility. You are looking at the former but not the latter. If he were a responsible person, then he should have improved his performance.
If, after giving a warning on his poor performance, he fails to improve, then either he is unfit for the job or lacks a sense of responsibility. If he is unfit for the job, then it showcases poor recruitment. The organization is responsible for wasting time and resources on this person. If he is fit and qualified to do the job but not performing, then he lacks a sense of responsibility. Why are you taking a guilt trip for his weakness?
"You can lead a horse to water, but you can't make it drink," goes the famous adage. Why feel sorry for a horse that prefers to be thirsty rather than move for the water?
Managers or HR professionals need to think from the head. Let the thoughts originate in the heart, but they should pass through the head. By removing the under-performing probationer, you will be doing justice to the organization. His removal will send a signal to everybody that your organization values the culture of performance. As an HR professional, you should put the organization's interest before the individual's interest. Therefore, go ahead and sack him if the situation merits sacking!
Thanks,
Dinesh Divekar