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There are three characteristics about enzymes that were somewhat puzzling:

1) Enzymes cause things to break down faster than they normally would.

2) In this process, enzymes do not break down themselves.

3) They break things down the most at room temperature and neutral pH's; they do not function well at extremes.

These are all characteristics of living things. The breaking down of hydrogen peroxide is like the process of consumption and digestion; looking at it this way, it makes sense that they are not broken down themselves in the process. Other living organisms also thrive in inverted "U" scales. Therefor, we think enzymes are very small living organisms.

To test this further, we could observe enzymes under a microscope and see if they appear to be improbable assemblies. Also, we could put them in an environment where there is nothing that can be broken down, and see if they are still around. If they are still present after being "starved," we would know they are not alive.