When attempting to resubmit failed tasks as a user other than the original submitter, by default there is no resubmit option available in View Submitted Tasks.
By design, only the original submitted can resubmit tasks. This applies to TEWS as well as through the user console.
If your screen does show the resubmit option it may be due to your customizing of the View Submitted Tasks, resubmit scope; "Resubmit Tasks and Events: No Restriction," which is not supported for TEWS, though it might work via the user console.
Only the user who initially submitted the task can resubmit the failed task.