My pump corrections weren't bringing my sugar down

I had a situation where my glucose kept climbing even though I had already given a correction through my pump.

Usually I expect to see some response, so when the number continued rising I started wondering whether something was wrong with the infusion set instead of the insulin simply taking longer than expected.

For people who use pumps, what clues have made you suspect a set or delivery problem? Do you have a routine for checking the site, tubing, insulin, or pump when corrections don't seem to be working?

This is one of those pump situations I want to understand before I'm dealing with it while stressed.