I often travel from Taiwan to China for short periods, and my last trip was to Shanghai just for the day. If my Taiwan visa has a 90-day limit per entry, did the day-trip reset the count?
Yes it did. Unlike many countries, Taiwan doesn't Limit your stay to 90 days per 180-day period, nor does it forbid visa runs. A number of expats live in Taiwan without a visa.
(note: you don't have a Taiwan visa for 90 days; rather, you can stay in Taiwan without a visa for 90 days)
Also, if you're a British or Canadian citizen, you can extend your stay by another 90 days with the MFA. Thus, you'd be able to stay for up to 6 months in one stay