"You only get stronger at rest" is a popular saying in the fitness world. In some epic contests, like the Tour de France, rest is often more emphasized than all the hard work of trianing. "The Tour is won in bed," said five time winner Eddy Merckx.
Admittedly that is an exaggeration, but recovery is a very important component of success in the program. If you train yourself to a point of exhaustion, you will need to recover properly before the next workout for the training to remain effective. If you don't recover well, you will get into a period of "over training", your results will plateau and the hard efforts you are putting into achieving your goal will stall out. Recovery is vital.
To be clear. Recovery doesn't mean rest. While rest is a part of recovery, so is alternate activity that can promote faster tissue repair. Recovery periods should typically involve a decrease in resistance work, but an increase in alternate activities (active rest) that promote faster tissue repair (stretching, yoga, light cardio). This Active Rest period also promotes gains for you in other areas, such as mobility, endurance, and static/stabilizer muscle strength.
Short Answer here is unless you are training for a specific event or performance goal (where your recovery will occur afterwards), working out 6-7 days in a row, indefinitely is not really sustainable and just a bad idea. So, if you are a "die hard" who is working out 5,6,7 times per week, doing doubles etc..., let's take a look at a better long-term solution for you to consider.
Periodizing your Schedule
Periodization is a process of training designed to build athletes to a performance peak while avoiding plateaus. Specifically, you should plan to train in various cycles only long enough for adaptation and growth to take place and peak, maximize your time at the peak then step back to an active recovery period.
A Focus on Recovery and Injury Prevention
Strategizing recovery protocol is a standard part of periodization athletic training programs, but forgotten by most do it yourself fitness enthusiasts. Recovery should always be a key component in the design of your fitness protocols.
Overtraining is more than just a risk in all training programs; avoidance can be a day-to-day struggle. You should make a mental note of this, you can only train effectively if your body is in a state where recovery is possible. What that means is that you should consider your frequency of training not just in terms of sessions per week, but sessions per month. A good practice, once you have build up the strength, capability and endurance to push yourself to 5 or 6 "Intense" sessions per week, is to establish a 5th week where you actively pull back on your level of intensity and either run through your sessions at 50% or engage in other varieties of activities. Consider this 5th week an Active Recovery Week, a gift to your body and well being (a great time for a deep tissue massage btw). By GIVING YOURSELF this recovery week you accomplish two things for yourself.
A chance for your body to go into a deeper more intense recovery and repair mode.
An opportunity to better prepare your body to accomplish even higher levels of intensity and performance after the recovery period than if you never took the time.
Both of these translate into stronger and more flexible physical performance as your training progresses.
The struggle for many of my clients is feeling like they are "slacking off" during the recovery week or "missing out" if they take a recovery week. Though it may feel like that in the short-term. The long-term benefits of this approach ensures that your body will be better equipped to handle a higher level of training in the coming weeks and more importantly your body will make more significant changes over time. Said differently, you get diminishing returns from consistent, non-stop training at high levels, and worst case scenario is this practice of unrelenting training can lead to a much higher risk of injury and debilitating fatigue.
Make the recovery week a reward for the last 4-5 weeks of hard training, use the time to get some good tissue work / massage done, engage in more active stretching time, get in a good long walk, add additional meditation time and so on. Remember why you are doing all of this work...to make sure you are strong and durable, not just today but long into the future. That is what I want for you.