My big guess is that after the 10th century, the flat round shield that we all know and love declines extremely for the use of the tear drop shield or kite shield. By the time of 1066, the viking style large round shield would be dropped in favor of the kite shield as evident in sources like the Bayeux Tapestry (I'm not mentioning Carolingian style concaved round shields). In martial practice, the kite shield is useful because it can protect your legs from a low strike, and its length could probably catch people into an immobile state that leaves them vulnerable for attack. Eventually, the kite shield offers that much of an advantage, the skill involved using a round shield with a center-grip is obsolete in some ways.
However, the large round shield with a center shield boss has been an effective tool through out most of Europe for centuries. It would make some sense that the viking style shield we know from archaeological evidence to be at least present in the 11th century.
Archaeological evidence:
Oseberg, Norway, 834AD
Gokstad, Norway, 900AD
Tira, Latvia, C9th
Trelleborg, Denmark, assumed end of 900AD
site source: http://www.vikingage.org/wiki/wiki/Round_Shields (Yes, I know, professor. Its a horrible source for citation.)
What I'm wondering is if anybody could provide evidence for flat, large viking round shields that is evident in archaeology in the 900A.D. in use past the 10th century? I'm guessing that some of the fanboys participating in the modern Battle for Hastings event have some horribly outdated equipment.