Sergeant Schlock is currently submerged in the Marinaris Reservoir. From the comic, it looks like he's pretty deep, and making no effort to surface.
The question is, how long can he stay down there? Well, OK, there are two questions here, and the first is easy. Based on Schlock's past extravehicular activities in space, he can survive, dormant and frozen in a vacuum, forever. So, I suspect he could stay underwater indefinitely.
What we don't know is how long he can remain active without oxygen. Does he require oxygen to function? He certainly needs a source of energy to drive his activities, and redox reactions make the most sense. How far do you suppose he can swim underwater before he shuts down?
What would be really cool is if he could use that chemical factory in his belly to split the water and survive off of that, or even just absorb dissolved oxygen, as fish do. Based on what we've seen from Schlock in the past, I see no reason why he shouldn't be able to do this. IF Howard decides to do this, color me impressed: these amorphs keep getting cooler and cooler, even after nine years.