In most any profession, things seem to get added to your schedule faster than they get taken away — so you tend to get progressively busier. For a consultant, the effect can be magnified when work starts piling up during the "feast" portion of the "feast or famine" cycle. You start to feel like you'll never get caught up, and that you should devote every available minute to getting all that billable work done.
But there are a couple of problems with that idea. First, there's the potential for burn-out. Even if you really enjoy your work, you can only concentrate on the same project for so long without a break. How long varies by individual, but everyone has their limit. You'll probably find that you're even more productive during your "on" time when you sprinkle in a little "off" time to keep you fresh.
Second, you can lose your edge. Consultants may be hired for their expertise on a specific topic, but they're also expected to have a broad understanding of their industry and of the available alternatives for any solution. That body of knowledge grows every day, and you need to keep up. It's not only fun, it's important to your career to spend some time learning new things. Yes, you can pick up a lot from the work itself — but clients' requirements don't usually lead you into all of the subject matter that you should explore in order to stay current.
So, I recommend that you set aside time in your schedule specifically devoted to learning something other than what you're supposed to be working on. Just as you're supposed to "pay yourself first" in your monetary budget, so you should make self-improvement a priority when budgeting your time. You can think of it as similar to Google's famous 20% time — although not everyone can free up one day out of five (or 20% of their potential revenue!). You'll have to decide how much you can afford, but during that time treat yourself as your own consultant, contracted to improve your skills.
Make sure that what you choose to do with that time solves both of the problems I mentioned above. It needs to be fun and interesting in order to provide a recreational benefit. It shouldn't be anything too close to your active projects. Rule of thumb: if your client would consider funding the activity, then perhaps it's too related. On the other hand, it should be something that's within the realm of what you do generally — or else it's a hobby that shouldn't be conducted during work time. If you're a software development consultant like me, maybe you'll sit down and finally take a look at that language or framework that you've heard so much about, or you'll implement something for your own use, or contribute to an open source project.
What's amazing is how this recreational work does "recreate" you. Taking a break and thinking along completely different lines often snaps you out of a brainlock. It can have the same effect as taking a walk or a shower, but with the added benefit of learning something new. And it's surprising how many times a seemingly unrelated endeavour will provide useful insights for your paying projects.