From what I understand, I see a couple different approaches, both involving a new table that has a Lookup column to the source table.
In one approach, you could simply add a new entry to the new table each time the button is clicked, with a date. Then you could do reports/summaries on that data however you want - weekly, daily, monthly, yearly. The downside could be if you have lots and lots of entries (thousands, tens of thousands), that you might run into performance problems. However this is a good flexible approach.
The other approach would be that when the button is clicked, check if the new table has a row for the current month for that source item, if not, add it. Then increment a number in a “Monthly Sends”.
I would aim for the first approach, since it cleanly records all sends as individual dated items and you can do with it what you want. If the table gets too long after a long period of time, you could consider processes to archive old data in other tables or other documents (using cross-doc).