Do you capture the timestamp in a dimension? If you do, and that timestamp contains the date, then you may be able to create a calculated metric using approximate count distinct. Note that you can use approximate count distinct with a classification of the timestamp dimension, which you'd likely need to do in order to isolate the "day" component. For example, create a "Day Number" classification to extract "05" from "2021.05.26".
This won't give you an average outright, but you can use it on a table with, say, Month on the y-axis to see a trend over time.
Depending on how many customers you have in this segment, it's distinctly possible that they show up every day of the month.
Since I haven't done this before, I'm working on this using my own data to see if it actually works as expected.