The sam3x data sheet leaves out that the dac can't go above or below 1/6 of the reference voltage. Other data sheets in the series have this limitation in the data sheet. So for vref = 3.3v your output range is from 2.76 to 0.54. Also, the a/d has errata as shown below.
I am sorry for a bit delayed reponse. I would to take your attention to Errata section from data sheet of SAM3X/A devices.
The latest data sheet is available from below link. http://www.atmel.com/devices/SAM3X8E.aspx?tab=documents
(I hope, you should have this data sheet already)
From the data sheet, from section 49 -SAM3X/A Series Errata, you can find three errata related ADC as mentioned below. (Refer ,Section 49.2.4 -Analog to Digital Converter).
ADC: First conversion after sleep
ADC: Last Conversion Error
ADC: Wrong First Conversions.
I believe the last errata “ADC: Wrong First Conversions”, might makes trouble in your board. Can you please check this erratum from data sheet and you have three work around mentioned along with these errata. You may please try one of this and check your ADC readings.