There is no direct option to pause an activity, since this would not really go according to the BPM approach for monitoring and controlling activities and their ontime execution.
Notice there are ways to handle these type of scenarios in which you consider that the activity can't be always immediately completed:
You could have notification alarms (http://wiki.bizagi.com/en/index.php?title=Alarms
), reassignment features (http://wiki.bizagi.com/en/index.php?title=Shapes_Properties#Reassign
), or you could even design this case in the model.
For instance, by using an attached timer event, you could set a time for which the task would go to another state if it is not completed (as in the example2 at http://wiki.bizagi.com/en/index.php?title=Intermediate_Event#Timer_Intermediate_Event
This other state can be desgined with an event, mainly since event do not have an expected duration because by definition we do not know when or if they are to happen.
See the image below for clarification:
Bizagi BPM Suite Support.