Hi Padraig, Ashik.
1. @Ashik The BAdI CRM_IC_INBOX_BADI is totally out as the method to compute deadline and priority is never called from ERMS. It is only called when receiving e-mails that do not use ERMS.
2. @Padraig Check the http://scn.sap.com/thread/3465037 thread where you have a 100% way how I solved changing e-mail priority based on senders address.
3. @Padraig If you still would like to use ERMS ActionHandling service instead of the BOR object delegation, use the suggestion from Ashik, but remember to change the priority of the first(previous) work-item (not current work item id) and I would also suggest to use the FM "SAP_WAPI_CHANGE_WORKITEM_PRIO" rather than updating the tables swwwihead.. directly.
Kind Regards,
Martin