and rebuilt alternator and still having an intermittent issue with low voltage
Most likely it's this "rebuilt" alternator. More on that in a minute.
@Dan Thomas will be along to offer actual constructive advice.
Here I am, and the advice will be the same as it usually is.
Cessna? This sounds like an OV sensor failure. Even if you have an aftermarket VR installed, it's quite possible that they left the original OV sensor installed and it's now malfunctioning and taking the field power offline.
He gets a voltage drop when he loads up the alternator. That means that the alternator can't keep up. More on that in a minute. The overvolt sensor shuts the regulator off if the voltage rises too high, lighting the panel light that was variously labelled "over voltage" or "low voltage," depending on the year. There was no difference in the system or function. That light will come on if the Alt switch is turned off, or if there is loose wiring or connectors or a bad switch or breaker in the Alt switch circuit. It will not come on if the alternator just quits, like it does in a car. The alternator could fall right out of the airplane and the light wouldn't come on. The modern ACUs (alternator control units) fix that.
Often overlooked is the Field CB and the ALT side of the Master.
These may be nearing 50 years old. Current to excite the Field passes through both of these.
The field current doesn't pass though the Alt switch or breaker. All that field switch does is turn the regulator on. The regulator has an "A" terminal and a wire goes from that to the alternator output stud, same stud that has the fat output cable on it. That A terminal feeds two things in the regulator: the voltage regulator relay coil, and it also provides the current for the field via the regulator relay contacts.
One has to get a look at the whole alternator-regulator circuit to understand it:
This drawing leaves out the master contactor and switch. I adapted it from the Ford car/truck system. The Alt switch is between the bus (battery) and the S terminal on the regulator, and you can see that it does nothing but turn the regulator's field relay on. The field current itself comes from the A terminal which, in the Cessna is connected to the alternator output. In a Piper it often goes to the bus. It gets the same information from either place. The field relay connects that to the voltage limiter relay via some resistors and stuff, and it goes through the limiter relay contacts and to the field in the alternator. When the voltage rises to the regulator setting, the contacts are pulled open and the field is shut off. The system voltage falls, the contacts close, and the voltage rises again. This happens hundreds or thousands of times a second. Even the newer electronic regulators use the off-on method of regulating. The field coil in the alternator smooths the flow, and the shutoff isn't total since the field is still connected to the system via the 10-ohm resistor. There are usually a couple of capacitors in the system to kill the electrical noise generated by that limiter relay and the field itself.
The alternator generates power using electromagnetism. Any time a magnetic field moves through a coil of wire, electron flow is generated is that coil. In the alternator, the magnetism comes from the rotor that is spun by the engine via a belt and pulley, or gears. The field current generates that magnetism in the rotor's coil, and more current means a stronger magnetic field. The alternator's output is dependent on three things: (1) the number of turns of wire in the stator (output) coils, which is something we can't change. (2) the speed of the field's movement, and in this case it's the speed of the rotor, which is directly related to the engine RPM. (3) The strength of the rotor's magnetic field, which depends on how much current the regulator feeds it. This is the handiest way to control the output of the alternator. As more loads are switched on in the airplane, the system voltage will fall and the regulator will feed more current to the rotor's field to strengthen the magnetism and make the alternator produce more current, keeping the system voltage up.
So electrical current has to be fed to that spinning rotor somehow, and it's done with carbon-block "brushes" that don't look anything like any brush. They ride on copper slip rings attached to the rotor shaft, and those slip rings are connected by wires to the rotor's field coil.
Now, to the real problem: that "overhauled" alternator. It will be a Ford alternator, DOFF10300-something. The Ford alternator has its slip rings immediately next to the rear bearing, which is a Torrington cup-type needle bearing with tiny rollers in it, lubricated by a tiny amount of grease. But the overhaulers all seem to make the same stupid mistake: they put a big gob of grease in there, and when the alternator is assembled and the rotor shaft goes into the bearing, much of the grease is squeezed out and it gets flung around by the spinning slip rings and gets on them. It mixes with carbon from the brushes and makes a tough sludge on those slip rings that presents a resistance to the electron flow from the brushes to the rotor's field coil. Now, no matter what the regulator does, it cannot feed enough current to the rotor to make its field strong enough to generated enough power in the stator coils to keep the airplane's system voltage up when additional loads are put on it.
I found this problem countless times in "overhauled" alternators, never in a brand-new alternator. The factories know what they're doing, and they even publish manuals that overhaulers are supposed to use on certified aircraft components. Kelly Aerospace was awful for this, then Hartzell, who bought them, and now I think it's Boeing, but the overhauling won't be done by Boeing techs. I filed endless SDRs on the problem, but nothing ever got fixed. There are also many independent overhaulers that make this mistake, too. It got so bad that I was taking apart overhauled alternators before I even installed them. I cleaned up all that grease, cleaned the slip rings and brushes. Then the thing worked like it was supposed to.
To find out if this is the problem, disconnect the field wire from the alternator.
Disconnect all the spark plugs, too. Put an ohmmeter across the field terminal and the alternator case, and you should find something in the neighborhood of 8 to 11 ohms for a 24-volt alternator, and that resistance should remain steady when you turn the propeller. If it's much higher than that, or if the resistance jumps around when the prop is moved, you have a grease problem. The resistance for a 12-volt alternator is about 3 to 5 ohms.
A side view of an alternator similar to the Ford. The slip rings are the blue things on the left. They're on the rotating shaft. The field brushes ride on them but they're not clearly shown here. There are light springs that keep them in contact with the slip rings. The rear bearing has that green shaft in it, which is just the same shaft as the rest of the orange thing that the pulley spins. Too much grease in that bearing just gets extruded when the shaft enters it. There should be just enough grease in there to fill the spaces between those tiny rollers in the bearing, nothing more.
That alternator in a car is usually running at about a third of the RPM it runs in the airplane, since in both cases they are geared or pulley-ratioed so that they reach their redline when the engine reaches its redline. The car is loafing along at a third of its redline, the airplane is at 90% of its redline. Those brushes therefore wear out much faster, which is why the alternator manufacturers recommend 500-hour brush inspections, and its also why those owners that ignore those recommendations have alternator failures when the brushes get too short and pop out of the their guides and the field dies. No more output. And a trashed alternator, since the springs then arc on the slip rings and ruin them, and you're buying another $700 alternator instead of replacing $30 brushes.
