So far, you've shown no indication that the 7805 types were behaving outside their specified limits. A normal 7805 is permitted to range 5% to either side of the nominal 5 volts. Most "5-volt" parts, taking this into consideration, are specified as operating within those limits.

I'm thinking that you have another problem. Have you set up one of these boards that has this low-voltage problem behavior with a high-current (e.g 20A) bench power supply driving the regulator output? You need a good feedback path to the supply, BTW, but that should tell you where the power distribution weaknesses in the hardware are located.

If the supply voltage to the supervisor chip is so low that noise and board-level voltage drop is an issue, then the problem is probably in the input voltage, the bypass, the layout, or perhaps in that the current capacity of the regulator is too low. These regulators have "features" that the designer must know and understand, e.g. short-circuit protection, thermal limits, etc. any of which might cause erratic behavior of the digital circuits. If, however, the input voltage occasionally drops below the, 2.2-volt, IIRC, (ripple, perhaps?) required margin the regulator WILL drop its output, and not necessarily in a linear relationship with the input voltage.

RE