Alternator not charging battery?

Hello, what makes you think it's not charging the battery? Is your charging voltage level around 12.4v at idle? If the charging voltage increases as you raise the rpm, then that is normal. Hondas are one of the charging systems that will drop the charging system voltage down to around 12volts at idle to help with fuel economy. It can be deceiving and look like you have a bad Alternator, but that's normal for that system. You can also turn on the headlights and some other components to load the charging system and the voltage should rise.
If the battery light is coming on, we can provide you will the diagnostic flow chart for trouble shooting the charging system.

https://www.2carpros.com/articles/how-to-check-a-car-alternator

When it's running, do a voltage drop test from the positive post on the Alternator to Battery positive. What do you get for a reading? Then do the same test from the Alternator case to battery negative.

Also, check the 100-amp Fuse 19 in the Fuse/Relay box under the hood. The flow chart for diagnosing the charging system states it requires the Honda hds or pgm tester, and also jumping out the scs line (which I believe is a communications line), so I'm hesitant on having you jump anything out like that, considering it requires a Honda scan tool to do so, we can do voltage drop testing to see if there are any circuit faults. What were the symptoms before you replaced the Alternator? And did you get a new one from the dealership or aftermarket unit?
Check the fuse listed in the section of flow chart below though.

So, all this started after replacing the Starter motor, and there were no issues before that?

I was just looking at the ELD, there's some basic tests to check its wiring to fuse 4 under the dash (pin1), its middle pin(2) which is a ground and the 3rd pin is the data pin to the ECM, but there are 2 different codes that would usually set with a failure of that component, the trouble is you're having to recharge the battery so much. All the service information is stating "check ELD data with Honda hds, and to use an amp clamp to verify current flow. There aren'tt any basic tests besides checking power from fuses, and if the eld was to set a code we wouldn't know because the computer's memory has been cleared by the battery being unhooked. There's a code P1297 eld circuit low voltage and a P1298 eld circuit high voltage. Each procedure starts with check eld data list with Honda hds or pgm tester. It's frustrating, unless you're a Honda technician, we won't have access to these scan tools. I think if it was a failure of the electric load sensor (eld) you would have had a check engine light on at first, and as battery voltage dropped off, the other symptoms you mentioned would follow. I will post the Flow Chart for the charging system just so you can see what I mean. But I don't want you to jump out any of these ECM circuits.

One thing it does say is, "Does the charging system indicator go off? Yes, Charging system indicator circuit is Ok. Go to the alternator and regulator circuit test."
So, the battery light is staying on, so next is "Troubleshoot the multiplex control system".

There is a TSB on the electrical system and the eld, but there is a code involved, Ill post it below. But there's always a chance of a bad Alternator, I know it tested good, but there have been a lot of bad parts lately.

Oh, then you need to have the system scanned for diagnostic trouble codes. A full system scan, not just the engine computer.

Well, since any codes for eld will be P codes, meaning powertrain, you can start with AutoZone or advanced auto and see if we get any codes for the eld, or anything else that may give us some direction with the charging system. Just don't let them tell you that you need this or that part. They tend to do that with any codes they scan for you. Just write down all the code numbers and we'll look up all the code setting criteria, if we don't find anything to do with the charging system and or can't go any further, then you can call around and see if someone will do a full system scan. Really, they shouldn't charge a lot, it only takes 10 minutes, but let's see what you get first with the ECM. P1298 and 1297 are for the eld. But with the eld codes, when they set the ECM usually will set the charging voltage at a set limit. Just try not to lose the memory by taking the battery out.

Hi Nateb88, just wanted to attach some images on how to do a voltage drop test. The first 2 images are from the battery positive to the alternator power cable. This is a good reading 0.04 volts with the vehicle idling. The last 2 images I took from the battery ground terminal to the body of the alternator. This reading is also good at idle of 0.01 volts.

Let us know what readings you are getting with the vehicle idling. Will keep an eye out for your response along with the fault codes you get once you do the scan so we can point you in the right direction.