iATS Scheduled job for recurring payments does not "finish" in the logs. How can I fix this or troubleshoot further?
a Couple of thoughts:


The Site URL is not the issue. Yes it has changed but I've confirmed
older URLs have not been deprecated - and are fully functional. 
I just verified on a site/project that Using 1.5.3, Civi 4.6.26 on D7 recurring job starts and finishes successfully - with a standard CiviCRM cron (set job to ON on scheduled jobs page)
You definitively want no PDF receipts to go out with your Email
receipts. If you are still getting DOMPDF errors - do you have any
other custom functionality that's trying to create/attach a PDF?
The recurring payments job - sends the tokens to iATSPayments -> and 
immediately receives a transaction ID. There is no IPN. 
Try this: go to your Reports -> Create Reports from Templates -> and 
go to iATS Payments Recurring Contributions Report -> Preview Report 
-> do you have any next scheduled contribution dates in the past? If so then let's try trigger them manually:
Go to your Scheduled jobs and on the right side -> hit Execute Now. Check the log -> did it run successfully? 
If not go to this Table: civicrm_iats_request_log and check to see which requests were made; then check the civicrm_iats_response_log for any answers from iATS.


Ok let us know what you find out.