Tickle for response

Tickle for response

I would like to do the following either through Business Rules, SLA, or script.  If the technician sends a response to a user, say asking for additional information.  and they do not respond in say 3 business days, I would like the system to send a reminder, asking for additional information again, I would like this to happen 3 times giving them 9 days to respond, if they have not responded in the designated 9 days, on the 10th day it would simply send a "closing ticket" message and set the status to something like "no response from user" which I can then just close as a batch when I choose.
If the user responds, this process stops.

This seems a normal process for many ticketing systems, so I am sure it's built in, I just can't find the right way to do it.

Technician sends response
   day 3 "reminder sent"
   day 6 "reminder sent"
   day 9 "Final reminder sent"
   day 10 "set ticket status to "No response from user"

User sends response
   Above process stops, user is not bothered until above process starts again.