non productive training ???

An Unproductive Training Status doesn't mean you're not training hard or well, it just means that the watch hasn't detected that your fitness metrics are improving due to the training (yet), but rather they may have taken a temporary dip. This often happens to me when I mix a hard Strength Training session in a day before I go for another run; the DOMS from the strength training means that the run is slower and 'harder' than normal and often an unproductive result appears in the Training Stutus. I agree that Unproductive is a overly negative word perhaps, but when you read the actual description in the link below it doesn't seem so bad.

https://www.garmin.com/en-US/runningdynamics/#vo2-max go down the page to the section on Training Status

Unproductive ? Your training load is at a good level, but your fitness is decreasing. Your body may be struggling to recover, so pay close attention to your overall health, including stress, nutrition and rest.

I should replace usual beer to still water after my workouts !!!

Water versus beer makes no difference to the recovery. But you won't care as much about your training status with the beer. :)

It means that your speed has dropped contrast to previous. Happened to me this summer too when got a slight flu and couldn't train as much as previously. What one can do in this situation is to keep monitoring the load and train according to HR to not strain your body too much and aid the recovery. Take the stress test before workout to make sure your body is rested and go easy if not just to maintain fitness. It requires patience I know. Hopefully pay off later again.

No point trying to be productive all the time. simply not possible.

If it doesn't improve may need to re-evaluate. Re-do LTHR etc.

Thank you all for your explanations. I took a little more than 2 days of rest and ran 7K today.
I got +9 in performance condition, ran my fastest kilometre,mile and 5 kilometres !
Finally I received a productive training with +1 in vo2max !

+9 ??? Wow, I've never seen anything above +5. That must have felt great!

I guess you're talking about the initial performance condition notification, which usually comes out somewhere around first 1K. I've seen similar values especially when rested. It usually drops quite quickly course of the run though. From what I've understood the value is simply your heart rate vs pace compared to your past performances so I think anything above 0 can be considered an improvement.

+9 throughout the whole run would mean quite a leap in fitness!

Well got +9 after 5 min run and then started decreasing slowly to +1 at the end of the course.
That's good indeed because I ended other runs with -7 or -8 !!!

High PC readings at the start of a run are to be expected, due to what is known as "cardio drift" - basically, your heart rate is lower in the 1st 10 minutes of a workout for the same output.