Clients will rarely leave a good service provider over a small rate increase. The top reasons are inertia and time. Clients rarely want to have to start looking for a new service provider, and they frequently lack the time to do so.
Beyond these factors, don't forget that if you're doing a good job as a translator, your clients know, like and trust you! Congrats. You're a known (and hopefully even cherished) quantity.
Think about a service provider you like—whether it's your hairdresser, accountant or financial advisor. Would you really leave them over a small price increase when everyone is raising their prices to stay in business? Highly unlikely.
You care about your relationship with your long-time service provider, and the last thing you want to have to do is hire someone new that won't have a clue (hey, that rhymes!). It can take a lot of time and effort to get someone up to speed on what you need (ok, ok, we'll stop with the rhymes... you get the picture).
By the way, there are lots of other ways to handle the threat of clients leaving you. You can always start with just one client to test the waters. Or offer longer deadlines.
Or accept that you might lose one client... and it might be the best thing that ever happened to you. Imagine having more time in your schedule to market to your dream clients! How would that change your business outlook, say, within 5 years?