My one month old Galaxy watch 3 often fails to record my heart rate while I am walking, biking or on my exercise cycle. In each instance I start the exercise right from the watch. During the workout I will look at the watch and see the heart rate is grated out and not updating even though the green sensor is flashing normally. Once I stop exercising the watch is then able to record my heart rate normally. I have done the basics such as making sure the watch fits well, checked the continuous monitoring option and even reset the watch. Nothing helps. I hope to get a real answer and not just a link to a page that tells me to do the things I have already done.
I too had this problem, and saw in a rather obscure post about disabling the "auto recognition" of exercises. I went through and everywhere I could find any reference to "auto detect activity/exercise", I turned it off. This is on the watch, Samsung Health, on both the watch and the Galaxy Wearable app. Mine would stop almost consistently at somewhere around 8-10 minutes. After doing this, I didn't have the problem.
I think that the system gets "confused" if you've manually started an exercise, and in whatever time frame the system sets to recognize an app, it decides "Oh, he's exercising, I'd better start this", and makes the initial exercise barf. Anyway, it made sense to me so go ahead and disable those things, be sure you reboot the watch and phone after changing the settings, and see if that doesn't solve your problem. It did mine.
Heart rate monitoring now seems to work during exercise since I changed heart rate monitoring when still from continuous to every 10 minutes. It may be a coincidence but that is what I am experiencing. I wish Samsung would monitor these posts and come out with a fix.