A limit is applied to the number of reminders that will auto-send for a single Client Task. After the fifth reminder to your client, they will stop.
This is implemented to reduce the likelihood of your emails to clients being blocked. Identical emails that are sent over and over again can sometimes be flagged by SPAM filters.
If you want to override this limit, you can re-send the Client Tasks and the count will start again.
How can I track outstanding Client Tasks?