According to the Wikipedia article on swans, swans are mostly monogamous but may sometimes separate, particularly after a "nesting failure". What "nesting failure" may mean is not entirely clear to me. Does it mean that they they have literally failed to build a physical nest? Or is it that they have failed to produce offspring? Or is it something else entirely?
Apparently it refers to the inability of nesting the eggs, because the nest was somehow destroyed, or environmental conditions were unfavourable.
I found a few examples pointing in this direction:
The Trumpeter Swan page on the Yellowstone National Park websites reports that:
From the abstract of: Nesting Ecology of Bewick's Swans on Vaygach Island, Russia - Syroechkovsky et al., Waterbirds, 2002
From this article:
Reproductive Success of Exotic Mute Swans in Connecticut - Conover et al., The Auk, 1999 (PDF)
Actually, nesting failure means that nesting trial fail before offspring could even leave the nest. In case of precocial species (where chicks leave nest immediately after hatching, like swans) it means that eggs was destroyed or parents abandoned nest, as @nico point out. In case of altricial birds (offspring stay in nest) nesting failure may also mean that all nestlings died before leaving nest.
for example among House wrens (Belles-Isles & Picman 1986):