Interesting problem. First thing to try is to use the signal-strength feature found in most TVs to measure the incoming signal on the NBC channel on both TVs.
It's possible that your NBC affiliate is the weakest at your antenna. The extra cable length to your downstairs TV could offer enough added loss to keep that channel below your tuner's threshold for reception.
Now, about your "signal amplifier." Why do you have it? Where is it installed? Unless you have demonstrated a need for a line amplifier, they sometimes cause more problems than the cure. If I was troubleshooting your installation, bypassing the amp would be my first step.
If your amplifier is not a pre-amp mounted on the antenna itself, as opposed to somewhere downstream in your cable routing, then that is usually a cause for problems.
If your antenna is aimed directly toward the transmitting towers and they're all in the same direction, there's no need to reorient the antenna.
Followup: there might also be a clue with regard to your specific NBC affiliate and your own location. Update your post with the channel number and city, or call letters, a description of your antenna installation, and your approximate distance to the transmitter site.
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Per your additional details. It still would be helpful to know the NBC affiliate info requested above.
However, your configuration there is very odd and has plenty of opportunity for improvement. First, I question the need for an amplifier on your cable system. You don't indicate how many output ports it has, but back when I had Comcast cable, I ran 4 TVs off of a 4-port splitter with no amplifier and good signal to all sets. Again, I would never install a line amplifier in a cable run unless its need has been demonstrated, and I don't see that in your case with the info supplied so far.
Also, is your antenna on a mast above the roof? You still haven't described your antenna installation. If it's on a mast above the roof and connected to your pre-existing cable run, you have a downlead going to your cable company's interface box, which is probably on a lower level or in the basement of your home. That means the total cable length from the antenna to the TV tuners is far more than it needs to be, probably way too much.
Cable Internet on the same cable system is a major confusion factor. That means you have another splitter in there somewhere, with another feed into your cable distribution. It would take a close examination of your configuration to tell for sure, but you could be injecting a mismatch in the line that's impacting the signal level to your TVs.
Ideally, your fix is an entirely new run of cable from your antenna, through a 2-port splitter, to your two TVs, using RG-6 cable and no amplifier. That would raise the signal voltage to both tuners, possibly enough to solve your NBC problem. The run from the cable interface box to your Internet modem should be completely isolated from the antenna-to-TV run.
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Per your last update. Well done on improving your cable runs and isolating the problem to one TV. Apparently, the tuner in that TV has a glitch on one channel. (You STILL haven't told me what channel the NBC affiliate is and where it is. It can make a difference. Long story.)
A digital converter might solve the problem but give you a new one. The digital converter will have its own tuner which, presumably, will receive the NBC channel okay. The bad news is those boxes only have an analog output, so no HD picture.