I 've been experiencing the exact same problem and up until today, always thought it was my ISP or WIFI.
When I try FaceTime on my WiFi, it works for about 10-15 min, then the video stops and eventually the call is dropped.
Today, I turned WiFi off, and had a nice long (2.5 hour) FaceTime call using only LTE cellular data.
I'm using an iPhone 7Plus 256GB running the latest at the time I write this 14.3 iOS.
I actually called my ISP to see if they could give me advice, they found this on-going thread in Apple Support.
On-going is NOT good Apple -- this has been a bug now since 2019 -- it's 2021 now!
I've been thinking of going Android for a while -- Siri's intelligence hasn't been updated EVER -- Homekit has the least amount of smart home tech -- iPhone's aren't innovative or exciting anymore -- just more expensive.
My first iPhone was the then top-of-the-line iPhone 4, and it cost a $300 without a monthly plan. Now, you want the latest top-of-the-line iPhone you'll easily spend over $1,200!
I know, Apple is targeting the upper-well-to-do-filthy-stinkin'-rich. They want to be an exclusive, pricy brand.
Fine. Go after those with deep pockets lined with gold.
But be warned Apple, it is one thing to design your products to smell like money. However, all smells blow away in the wind -- especially when that wind is tainted -- cheapened even -- by hardware and/or software bugs that don't get resolved YEARS -- if ever -- and by ever I mean never?
Seriously Apple, I've been a loyal Apple customer for YEARS.
But as I watch Google, Samsung and LG continue to innovate, and more importantly, to introduce products that are more functional, more reliable and cost a LOT less than yours, I'm thinking this is the end of the line for me and Apple.
And I'm not alone. Just look at how many Apple customers have clicked the I have the same problem on this thread. (As I write this it's not in the tens, or hundreds, its in the THOUSANDS.
Sad.
Pathetic.
Hey Google, look out -- here I come.