For a lot of the activity curves, although they appear to be increasing, you can't really say they are because of the error bars of the measurements (for example, the blue and orange lines in the alpha-amylase graph). But there clearly are some enzymes whose activity apparently increases. Here are some troubleshooting questions:
Were all of the enzyme assays performed at the same temperature? Was enough time/a consistent time given to allow the 40
o and the samples to equilibrate to the assay temperature?
How did you assay the activities of these enzymes? Were the substrates made fresh the day of the assay? Could the spontaneous degradation of your substrates account for the apparent increase in activity?
Some proteases are zymogens (
http://en.wikipedia.org/wiki/Zymogen), and the activities of these enzymes would be expected to increase over time (though I'm not sure you'd see the increases you are seeing). Is your bacterial protease a zymogen?
Are you sure that there is a consistent amount of enzyme assayed at every time point? If the amounts of enzyme vary in each sample/preparation, then you should probably look at specific activity (units/mg) and not just activity.