Given that the lightning connector is the hardest working part of the phone, generally being plugged and unplugged at least once a day if not more, it stands to reason if anything is going to wear out, it's going to be that plug.
Based on your description, it really sounds like your port has seen better days and should be replaced. I'm assuming here that you've tried all of the non-surgical remedies such as trying a different cable and cleaning and inspecting the port for any damage or obstructions like lint or dirt build up inside.
Unfortunately, iFixit doesn't have a guide to that repair, but the Spanish site Nadie Me Llama Gallina has just what you need. As you might guess, the site is in Spanish but does have an English language option.
Manuales / Apple iPhone 12 Pro / Load flex - Nadie Me Llama Gallina
I would definitely recommend replacing the port, which should get you fixed right up. If you want to support iFixit's repair efforts, you can purchase the part you need right here on this site.
iPhone 12/12 Pro Lightning Connector Assembly
If you're a bit more cost conscious, you can also find it on the major retailer sites like eBay, Amazon and AliExpress, plus a host of other places that specialize in phone parts.
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