IG,
Not sure this has anything to do with your issue but it is something I seem to consistently hear with what I read on people consistently missing to one side and tips from pros. It may be a matter of eye dominance, and knowing how to read a putt and setup with that in mind. Make sure you are using your dominant eye. The majority of the population is right eye dominant and will have a tendency to miss right. Being that it is early in the year, I would just guess you may be right eye dominant. As many have hinted in joking, although has some merit, as the year goes on you may likely adjust for this and tend to miss left.
The article below just kind of explains the idea, and is the first I saw. You will likely find many about this if you do a search. I also tend to make sure my dominant eye is in line with the ball and the hole when I read the putt and notice I miss to one side. From what I hear, people who putt right handed and are left eye dominant have a real advantage with putting. For which may explain why I am fairly happy with my putting as I am left eye dominant.
IMO, it is certainly something that is worth knowing though.
GOLFONLINE - See The Perfect Putt
I believe this is also part of the basis on the quiet eye approach to putting or many of the other unique approaches to putting, where it opens up the right eye to better see the line and the hole for putting for people who are right eye dominant and putt RH.
edit 1 - in all honesty, if I consistently had putting issues and was looking for some kind of change, and was right eye dominant, I would seriously consider putting LH. But that is probably a fairly extreme approach. Then again, it is no less extreme than what I see many times where people may go through 3 putter in a year to tackle the same issue.