Check if the user you are running the script as (if you are using one) is an admin on the server; Check if the arcpy license is active for that user while not logged in. One issue I had was trying to import another script using 'from <folder> import <module>. Worked in the IDE, but in the task scheduler it failed. Had to use just import <module> for it to work in the task.
You can run some test tasks to get exceptions as well to help troubleshooting.
try:
import arcpy
from arcpy import env
import os
import sys
from datetime import datetime as dt
from datetime import date, timedelta
from subprocess import Popen, PIPE
... try other things
except Exception as err:
# write the err to a log
f = open(os.path.join(r'c:\Tasks.txt'), "a")
f.write(err.message)
f.close()
