Yes, unfortunately Hostgator is one of the worst offenders for this, as you will indeed have to pay their $10 fee every time, so at a minimum, $40 a year (if you do wait til the last minute.) For that reason, it’s usually cheaper to pay for 1-year validity commercial certificates instead, or switch away from Hostgator, and tell them why you’re leaving if you do.
You can renew at any point, technically, as long as you don’t break the rate limit of 5 identical certificates per week, or 20 certificates per base domain per week. Typically, the recommendation is to renew every 60 days, so you have a month to figure out anything super broken. Of course, with Hostgator, this would mean that you would end up paying $60/year in support fees. =\