Currently, as per the Jira functionality, when the date of the action is <= 7 days ago, you’ll be able to switch between relative and absolute formats by clicking on the timestamp. 

Therefore, Jira sometimes chooses the least useful relative date, as an example: 

• An Issue action on Sunday, December 30, 11:59 PM.
• Look at the item on Monday, January 1, 12:01 AM.

Some relative times could be applied in these examples: 2 minutes ago, 1 hour ago, one day ago, or one year ago. Jira chooses the one-year-ago option, but the most useful choice would be two minutes.

Solution

So a solution would be to implement the ability to choose between these relative dates options.