Unable to re-trigger or test one of the Robotic Tasks

Your issue is most likely a stuck/queued robotic task or no available robot, so the process stays active and times out after 96 hours.
https://docs.appian.com/suite/help/26.3/Execute_Robotic_Task.html#runtime-behavior

Also, Verify the concurrent execution limit setting on that robotic task - if it's set to 1 and a previous instance is stuck In Progress, new ones queue indefinitely, which matches your exact symptoms (no error, just hangs then times out).
https://docs.appian.com/suite/help/26.3/rpa-9.22/configure-run-time-settings-tab.html

https://docs.appian.com/suite/help/26.3/rpa-9.22/robotic-task-execution.html

Removed all the older executions of that Robotic task still the issue persists

Did you try to debug or test like this? docs.appian.com/.../robotic-task-execution.html

Yes, nothing happens, no execution gets created in operations console. Robot is online and other tasks run as expected on testing or debugging except this particular robotic task. I would really appreciate if you can suggest a solution to handle this

If An execution instance is not getting created it is weird indeed and I have never faced this with my limited experience with RPA. I can suggest few things as of now, that you can try. 

1. If recently any modifications are made to the Robotic task, then revert it back to the version before and try to run the task.  
2. If no modifications are made, then see if recently you had RPA upgrade/any hotfix deployments done that might have as regression impacted this behaviour. Appian Support team should be looped in on this issue in this case for resolution.
3. The Robotic task design, whether its in a loop or a subtask of another robotic task etc might be impacting the debugging. As a note, The debugging execution automatically pauses at the beginning of the Setup and Main sections. So go through this documentation here to debug the robotic task with various debugging options available and try to find the root cause. 

If none of the above work then better to reach out to Appian Support to investigate the matter.