Trigger survey from Custom Event Handler or Reports

Summary

Trigger survey based on certain conditions

Content

Hi 

currently we are triggering survey from business rule when the incident is solved and after 96 hours. This was working fine. But business came up with issue if a customer replies to mail this was making the incident open and cannot be treated as solved incident. 

I need your help to arrive at  a solution where an incident is in SOLVED status for CONTINUOUS 96 hours without a status CHANGE survey need to be triggered.

Please let me know your ideas to solve this issue. Need the solution urgently.

Thanks in advance

Kind Regards