If I take up a special offer before my membership expires, will I lose the remaining time on my account?

No, you will never lose any remaining time you've previously paid for. You will be sent an email from Apple/Google Play telling you an auto renewal has been set up to start in 12 months or 1 month's time (depending on which subscription you purchased), but you haven't lost any remaining time on your account, this is locked onto your account. As and when you decide to cancel the auto renewal in the future, your remaining time will be used up first before your account closes.