Hi Amol,
Technically this would definitely be possible. I'm sure you don't want to implement a procedure like this from a process/business perspective.
If you want to follow up on certain issues, just put a value in the due date field, create a JQL filter showing the issues with a due date today or e.g. coming up in the next couple of days. Then use the JQL filter to show the list of issues to follow up on a dashboard. You might also use filter subscriptions to send a periodic digest of issues that need follow up by email. Check the documentation on working with search results for a bit more background.
I would advise you not to tackle your question in the way you are suggesting, is because by resolving an issue, you actually state that work on that issue is done. Than reopening the same issue again indicates that this is actually not the case.
I suppose you are actually trying to find a way to manage recurring tasks. You might take a look at this related question to find more inspiration as well. Or if you want to go down the path you suggested after all, you could do so with the Automation for JIRA add-on (even with the free Automation Lite for JIRA version). All you would need is a Reopen transition in your workflow and an automation rule based on a JQL trigger on due date to execute the transition.
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