Hard to say, some article I read said that they would run out of cash in early 2013. But if their 2012 releases fail badly, who knows. South Park itself has the potential to be a huge success for THQ (depending on the deal with South Park Studios & Obsidian ofc).
I doubt they would fail outright anyway, their market capitalisation is very low so they'd make a nice target for a competitor to buy- it would be less than 10%* what EA paid for Bioware/ Pandemic for example, and given that they could then rationalise the distribution side of things plenty of savings could be made.
*They'd have to take over the debt/ liabilities as well, presumably, which would up that.