This was the subject of a recent review in Advances in Chronic Kidney Disease. From the article:
Cirrhosis is characterized by systemic and splanchnic vasodilation that leads to excessive nonosmotic secretion of vasopressin (antidiuretic hormone). Hyponatremia is a common electrolyte abnormality in advanced liver disease that results from the impaired ability of the kidney to excrete solute-free water that leads to “dilutional” hyponatremia—water retention disproportionate to the retention of sodium.
The excessive vasodilation is mediated by nitric oxide (NO). NO synthesis in endothelial cells of cirrhotic patients is induced by high levels of circulating endotoxins translocated from the gut having bypassed the portal circulation.
Besides non osmotic vasopressin release the paper also mentions impaired water delivery to the thick ascending limb of the Loop of Henle as a contributing mechanism.
More from the paper:
Hyponatremia in liver diseases carries the prognostic burden, correlates with the severity of cirrhosis, and, in recent studies, has also been implicated in the pathogenesis of hepatic encephalopathy.
Hyponatremia's contribution to hepatic encephalopathy is complex. Not only do the manifestations of hyponatremic encephalopathy overlap considerably with those of hepatic encephalopathy but hyponatremia is contributory to the pathogenesis of hepatic encephalopathy itself by multiple mechanisms. One of these involves the exhaustion of certain astrocyte functions as a result of the extrusion of ions and organic molecules as an adaptive response to hyponatremia.
As a prognostic indicator, hyponatremia is associated with hepatorenal syndrome and spontaneous bacterial peritonitis.
Although hyponatremia is associated with adverse outcomes in cirrhosis, at what level one should attempt to raise the sodium and by what means are unclear. The article recommends against the use of demeclocycline to treat hyponatremia in cirrhosis despite its popularity in the treatment of hyponatremia of a variety of causes.