Auto move a Sheet after x# of days of inactivity

There is not a way to automate it, but it is a good idea. Feel free to Submit a Product Enhancement Request.

In the meantime, you could use two additional columns. The first would be a Modified (date) system type column.

The second would be a regular date column.

Assuming your inactive period is 30 days (if more or less just replace the 30 in the formula with the appropriate number), you could use a formula in the regular date column to look at the most recently modified row then add 30 to it.

=MAX(Modified:Modified) + 30

This will produce a date that is 30 days beyond the most recent modification. You can then set up an automated reminder set to send on a date in a cell and select the regular date column. The reminder will alert you that the sheet has been inactive for 30 days and is ready to be archived.

If any row within the sheet is updated, it will update the formula and push the date out further, so you don't have to worry about a stale date triggering an archive notice.