I haven't noticed an excess of replies to your concern, but it seems you are not alone with the problem, as I just used your phrase above to do a web search: 'Fitness widget on my iPhone doesn't refresh as I'm exercising unless I quit it and start it up' and that gives lots of similar hits with those with the same problem and very few if any actual solutions.
What's interesting to me and I find a bit troubling, is that Apple appears to be rather slack on getting a solution as the same problem seems to have been going on for several years now. A Restart for a solution that you discovered seems to be the only solution for now that I could see which seems to be rather excessive for a fix for a problem that shouldn't even be there.
Anyway, I hope you find the exercise beneficial regardless of what the widget says or doesn't say...
- Patrick
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