In a 2007 story for USA Today, it was published that the odds a player returns from a second Tommy John surgery to a pre-surgery level of baseball is roughly 20%. Granted there have likely been further advancements in the procedure over the past five years, but the odds certainly aren't on Joakim Soria's side this time around.
Two pitchers that came to my mind who did have success at the major league level after a second Tommy John surgery were Doug Brocail and Chris Capuano.
Brocail, who retired after the 2009 season at the age of 42, had the surgery twice. Because of this he appeared in just three minor league games total from 2001-03. Though Brocail was never at the level that Soria once was, Brocail was a first-round draft pick in the 1986 draft out of high school. Post Tommy John surgeries he enjoyed modest success, including a solid 2007 season with the San Diego Padres in which he was 5-1 with a 3.05 ERA and 1.17 WHIP.
Another player whose had modest success after having the surgery twice is Los Angeles Dodgers pitcher Chris Capuano. He went under the knife in both 2002 and 2008. At the time he was 23 and 29 years old, or similar to Soria's time frame. He is the rare pitcher who has actually performed roughly the same after multiple surgeries as he did before.
However those two are true exceptions, as Jose Rijo has the operation performed five times and was never able to get back to what he once was. There are numerous other examples of pitchers who had failed attemps after even just once Tommy John surgery.
The future doesn't look bright for Joakim Soria, but there is the outside chance that he could be one of the few who is able to come back a second time. However I wouldn't exactly count on it happening.