At the risk of stating the obvious, getting sick or injured is the best way to bring your training progression to a screeching halt. Fortunately most illnesses and injuries are preventable.
Avoiding ego-driven training can prevent many injuries. If your sparring partner catches you in a submission, don’t be a hero – just tap out. If an injury starts bothering you when you are doing an exercise, stop or modify the exercise.
The important thing to remember is that you are training, not fighting, and that the purpose of training is to learn. There is no better way to prevent learning than sitting on the sidelines nursing an injury.
The best way not to get sick very often is to avoid overtraining. Overtraining occurs when the amount and quality of recovery time is insufficient to fully recover from the stresses of training. In other words you are putting too much strain on your body for it to recover properly.
Overtraining can be remedied in two ways: less stress and/or more recovery. The first cure for overtraining is to cut back on the stresses on your body. This might mean not training as much, not working as hard at your day job, going for easy jogs instead of hard runs, etc. The trick is to train hard enough, but not too hard, for your current level of fitness. This is a difficult, but worthwhile, balance to achieve.
The second cure for overtraining is to improve the amount and quality of recovery time. Sleep more. Relax more. Do more yoga and massage. Improve your nutrition. Sleep is probably the most neglected element here: there is a lot of research suggesting that most athletes need a lot more than 8 hours of sleep a night for optimal recovery.