Over-exerting tired muscles and tendons can lead to muscle pulls, over time it can contribute to Repetitive Strain Disorders such as Carpal Tunnel Syndrome and Tendonitis, and, believe me, you don't want to suffer from these. The best thing to do is prevent the cause any factors that may contribute to pain. If you don't know how to warm up, contact a local coach, physical therapist, or sports doctor. There are also a number of good books on stretching, which is what you want to do, ever so gently. There are great benefits to warming up, warm muscles will perform better than cold muscles, you will get more out of your workout.
Relaxed muscles react better than tense muscles.
Relaxed muscles, IMHO, will not tire as easily. To this end you can do quite a bit that will benefit not only your juggling but your life as well. Meditate, take up Yoga, Take up Feldenkrais. I recently restarted Alexander technique after a 15 year hiatus. It really helps keep my body relaxed at all times.