Automated Reminder Emails to Clients

I am looking for a solution for this issue. I manage several hundred clients, and it is pretty common for our clients to constant need reminder emails sent to them. Our current system is to manually select the reminder the client needs, then write the email, then email the client. What we would like is to have a system in place that automatically emails the client based upon what the client needs to be reminded of, when they need to be reminded.

For example:
Let's say we have 100 clients
Those client needs to be reminded of 1 different thing each month throughout the year
How could I automate reminded them?
For the solution to be 100% effective, it could 'detect' which clients need reminding and which ones don't
It would also send the email reminder at the appropriate time
Lastly, it could repeat a reminder every so often, until that client no longer needed reminding
For example, the client forgot to sign an Authorization form by Jan 1st. On Jan 2nd, the system would send the reminder, if after 2 weeks the client still did not send in the form, the system would email alert the client to send in the Authorization form.

Thanks for the help. I assume there must be systems in place that resolve this need, I just don't know where to look.

Thanks.