JO Triggered PX engagement - don't show after X days even if still qualified

We have a JO set up in Gainsight CS that triggers a PX engagement for renewals. 

Internal process:

1. JO trigger engagement for past due renewals
2. Audience rules in PX set to only show for those in the “PO Sent” status

Let’s say 3 months pass and the person never logged in during that time period. They have also paid that PO since the engagement was triggered. Then a new PO is created for the year, and they are once again in the “PO sent” status. Technically, they would qualify to see the engagement since they meet the PX audience rules once again. 

So my question is, can we set some sort of audience rule to say “If they have not seen the engagement within X days of being triggered via JO, remove from engagement?”

Or is there another way of looking at this?