Mine expires at the end of April. I figure I'll call in January. My city is pretty busy but since they removed the grace period expiration it really doesn't matter anymore just as long as you're in before it actually expires. Keep in mind as long as you file the paperwork before your current license expires they no longer limit the grace period. Up until a few years ago it was 90 days. Your current license, even expired, is legal to carry on. You won't be able to buy any new guns in that time though.
As far as losing a year it's definitely possible and happened to me on my first license. I applied in Feb, issued in March, and my bday is in April so my first "year" was only about 4 weeks long. So, what the officer is telling you is true. Your license starts on the day they printed it and always expires on your bday. So, if you went in today and they get your new license printed before your current license expires, you'll lose a year. I don't know if it's possible because I've never seen it but if a town can print your renewal "issue date" as your bday as well you'll get the full 6 years. I think it depends on the city or town and how they process them. I was told by the person handling the licenses, in my city, they have since corrected it so you no longer get the "short years" like my first license. My last renewal though they were really busy and didn't get my license printed till July. I was covered by the race period, at the time, but my issue date says July.
Example: Let's say you went in today and your current license expires 1/15/19 but they printed your license on 12/15/18. In that case your license would expire 1/15/24. If you went in on 12/28/18 and they didn't print your license till 1/16/19 you would still be covered on your current license but your new one would expire 1/15/25.