This is a common and important question that I have asked many other photographers and business owners. I am not just referring to the date, I am also referring to situations that would facilitate a price increase. Lets assume that you are already confident that your work is definitely due for a price increase.
1) When you have at least three months bills in the bank This is probably my least favorite situation, mainly because it is an indirect result of your profession. It is also not the most confident reason. You are basically bracing for a major drop in sales due to your sudden rise in prices. I would encourage photographers to have at least this amount in savings ANYHOW as sales can have highs and lows depending on the season.
2) When you get a new certification or accolade I love this situation. I believe it works for you on so many levels. You have mostly likely educated yourself in doing this and have added value to your work. Kudos! You should definitely let the world know what you have done (humble brag) to promote confidence in your business. It also gives you the confidence to raise those prices and stand up for them.
3) Every dang year I believe any business, large or small, should give their employees raises every year as long as they are in good standing and the business has turned a profit. That would include the business owner. Its good to be consistent with the amount and timing of this to train your clients to expect the price change. I believe the best date to do this is right after tax day in April and the second best date is the new year.
You may lose a few clients and that is ok, they probably werent clients you want anyway if they are willing to jump ship over an incremental rise. Now, dont go over board unless you are prepared for the results. I had one client complain about the change and they started using another photographer. As their needs got more sophisticated, they came back for one shoot and have stayed ever since. I won. Also, you dont need to make a major press release about your price change. Update all your price lists and do business as usual. Your VIP clients probably dont look at your prices every shoot and wont mind the change.