To "stumble along (as best you can)" is a metaphorical expression that means to "continue despite obstacles or incapacity".
Imagine, for example, that you are running a race but along the way you hurt your leg. You are determined to make it to the finish, so you stumble along, as best you can, until you get to the end.
In this context the author is saying that the switches have a choice when dealing with subtle errors. They can shut down (which would make people think the switches are crap) or they can try and handle the errors so that they keep working anyway, even though the signal might be corrupted. Metaphorically it's like a runner stumbling along, hampered by some injury, but still trying to move forward.
Of course, the errors might become too severe to continue, or the data might get seriously corrupted, but I'm sure the book discusses that later in the chapter.