I've been freelancing for 35 years, so obviously I've had to deal with multiple rate increases over the years.
Rather than increase my rate every year or even two years, which seems somewhat petty, I usually wait a few years and increase my rates by a higher percentage.
I have both long-term -- some more than five years -- and short-term clients (a few months). I will typically increase my rate for new short term clients first, but not for any current ones (either short-term or long-term). Such increases will typically be 20% or so over my previous rate. Of course the new client won't know what my previous rate was. Eventually the short-term clients billed at the now lower rate will all drop off.
About a year later, I will send a letter (well, now an email) to my long-term client(s), saying that I have increased my rates and have been billing such and such an amount over the last year. But since they are a long-term client, I will be billing them at only 90% of the new rate. I am still getting a substantial rate increase for my long-term clients, and they see they are getting a better deal.
I've never had a client drop me because of my rate increases as far as I know. Then again, I'm probably billing a little bit under market.