Hi @Emma_Ramirez , welcome to the forum 
The issue sounds like it has to do with the relationship between the rule creator and the template owner and members when a new project is created.
In each rule’s setting (top right of each rule’s editor, the 3-dot menu) make sure that ‘only you can edit this rule’ is WITHOUT a checkmark.
This should allow the rules to be adopted by the new project owner and therefore should not pause them.
Try it out and let me know if this issue still persists!
PS: you can read more about a similar issue here: Include rules owned as part of deprovisionning a profile - #8 by Emily_Roman