I've had my Gear S3 Frontier watch since about 9/2017. Only in the last ~6 mos has the Home button stopped working. Holding the Home button down for about 10 seconds did not work for me but pressing the Home and Back buttons simultaneously and very briefly works like a charm. My current working theory is that one should then hold the Home button down until the watch reboots (and remember to change your Display timeout settings back to whatever they were-10 secs for me).
I agree that the problem is probably some sort of software/firmware problem as although the Home button would rarely work when the watch was just sleeping and should wake to the clock face with a Home button press, at other random places in the watch interface, even with the Home button not working to wake the watch, a press of the Home button would jump the watch back to the clock face. So, yes, Samsung should fix this problem to give us the years of life we expect from such a relatively expensive device. It's not a $30 throw-away-once-a-year Timex watch.
BTW, the Home button problem made me realize that the ultimate life of this very lovely watch depends on the mechanical life span of the two physical buttons and to a lesser extent, the rotating bezel. So I've now set Touch-to-Wake as my normally-used alternate to pressing the Home button. I had it off before for fear that I'd be turning the watch on and off all night in my sleep by brushing the watch face against my face, the other arm, etc., but that doesn't seem to be the case, and now that I've gotten used to tapping the screen, it's my preferred method of waking the watch, which I normally keep Display Off to maximize battery charge for the day and long-term battery lifespan.
One further thought is that perhaps the Home button app problem arises from running some other app that's somehow consuming Home button presses or interfering with them reaching the OS interface for that type of event. Perhaps Samsung should add an interface to its Galaxy Wearable phone app that allows one to examine (and configure) the use of the watch Back and Home buttons according to OS/app context?
Please press both buttons to go to the power off screen. Also press both buttons to turn on. I think one of the updates have changed the power off/on algorithm and now includes both buttons.....or it''s a work around in an update to solve the lower button problem.
I concur, they are on the flex board, very small 0201 size. But the are not capacitors, they are 0 ohm resistors. I found that the connections from the buttons to the resistors were good but both connections from the home key resistors to the watch were bad on my watch. I soldered very thin magnetic winding wire directly from the switches to the watch. The home button goes to the innermost pad on the watch board, call it pin 1, and pin 3. The back button goes to pin 2 and 4.
Another option is to solder on a new flex button board. They are on eBay https://www.ebay.com/itm/153118442631