We were there in Nov 2013 and I can confirm that the fort IS closed on Mondays. We visited it then and spoke with the Pakistani guard on the gate who let us take a couple of interior photos from it. I guess the main thing we missed was the Thesiger photo exhibition. Apart from a couple of structures in 2 corners it consists mainly of a large courtyard. Perhaps also it is possible to go up into the 4 story tower. If you can't get in then the external views are still worth having.
Unfortunately I don't have personal experience of it on the Sunday - however I DO have the Fort Brochure picked up in the National Museum and it clearly states
"Open Daily except on Mondays
Entrance Free of Charge
Tuesday to Sunday 9.00 am - 5 pm"
The National Museum WAS open on a Sunday (I preferred to spend my late pm there after driving from Dubai via Abu Dhabi as it too is closed on a Monday) and I don't believe that closing on a Sunday is normal/common in the UAE but I cannot of course be 100% certain in this case. Sorry!
For certainty you could try e-mailing the Abu Dhabi Authority for Culture and Heritage which is apparently responsible for the fort
firstname.lastname@example.org (according to my brochure)
email@example.com (according to the Abu Dhabi tourism and Culture Authority's web site!)
Indeed I see that this latter actually has a contact form for making enquiries!http://tcaabudhabi.ae/en/about/Pages/contact.us.aspx
The Hili Archaeological Park was open on the Monday by the way - it had a gate and an "office" with a window which might once have been intended for taking money but it was unoccupied and seems to be a fully "free" facility!!.