"Scientists do continually try to measure the constants of physics, but the usual motivation is to get more precise values, rather than to check whether those values have changed. If you had a technique to measure the speed of light that was no better than one that was previously used, you might not bother to make another measurement unless there were some reason to believe the previous value was in error. Moreover, if you did measure the speed of light and got an anomalous value, the odds are good that you would conclude that you had made a mistake in the measurement, rather than that the speed of light 'hiccuped' that particular day. State-of-the-art measurement techniques are extremely complex and require all sorts of checks to be sure they have been performed correctly. If in fact the constants of nature were changing, it would be very difficult to know how precise your experiment needed to be to detect such a change, unless you had some way of estimating the expected rate of change. Random, occasional hiccups in the constants almost certainly would go undetected.
"The physicist Paul A. M. Dirac once suggested that the universal gravitational constant, G, that measures the strength of attraction every particle of matter feels for every other particle was actually weakening with time, in proportion to the age of the universe since the big bang. According to Dirac's theory, the force of gravity would be only half as strong in 10 billion years as it is today. Given this specific prediction of the rate of weakening, scientists could make a specific test. The moon's distance from the earth is understood to be slowly increasing because of its tidal interaction with the earth (as tidal friction slows the rotation of the earth, the size of the moon's orbit must increase to conserve the total angular moment of the earth-moon system). If gravity were growing weaker with time, the moon would recede from the earth even faster than conventional theory predicted. Precise timing measurement of laser pulses from the earth bounced off reflectors that the Apollo astronauts left on the moon shows that the moon is indeed slowly receding but only at the expected rate, not the faster one Dirac's theory would imply.