Rolling average producing a tail

Here's your measure:

// 1st basic measure
[Total Amount] =
	SUM ( 'Fact Daily Readings'[Amount] )

[30 Day Rolling Average] =
var __lastDayWithAmount =
	lastnonblank(
		ALL( 'Dimension Date'[Date] ),
		[Total Amount]
	)
VAR __lastDayVisible =
    LASTDATE ( 'Dimension Date'[Date] )
var __shouldCalculate =
	__lastDayVisible <= __lastDayWithAmount
var __startDay =
	// YOU SHOULD BE CAREFUL WITH THIS
	// SINCE THIS OPERATION MIGHT GET YOU
	// OFF THE LEFT BOUNDARY OF THE CALENDAR.
	// You need to check if this date is
	// not BLANK. If it is, it means you're
	// off the calendar... and can't calculate
	// your measure.
	DATEADD ( __lastDayVisible, -29, DAY )
var __periodToAverageOver =
    DATESBETWEEN (
        'Dimension Date'[Date],
        __startDay,
        __lastDayVisible
    )
var __result =
    AVERAGEX (
    	__periodToAverageOver,
        [Total Amount]
    )
return
	If( __shouldCalculate, __result )

This should work. If it doesn't then some small modifications might be needed.

Best

D