VO2 Max always 45!!!!

Which activity are you using ? If you use Trailrunning there will be no update on VO2max.

It seems not all types of activities will contribute to the change of VO2, but Run would be one of in the list contributing to VO2.

When I did "climbing", no matter the tough and frequency, no help to VO2 at all.

I am running my a** off with the 5 Plus but no effect on the VO2 Max....

You do realise that VO2max is a fitness metric and not a measure of intensity?

Constantly working out too hard can actually be quite counterproductive in regards to gaining fitness.

Check your heart rate zones and set them adequately to your case. I had a similiar issue to yours and after setup I managed to finally move my V02 and training status ;)

You may have reached the maximum level of your VO2max. It's not a metric that will continue to increase. Gains are biggest for the least fit then decline to non-existent or very minor for the very fit. Furthermore, as you age the maximum you can expect to reach will also decline.

Once you reach the level where gains in VO2max diminish you need to begin to focus on how you can expand thresholds like your anaerobic threshold, your lactate threshold, and your efficiency.

Ok Guys, here's what I did:

I reset the Watch and entered my personal data, adjusted the heart rate zones and everything else.

Then I went on 3 runs during the last 7 days. Below you can see the records of the runs which I find to be enough for a new computation of VO2 Max. But the VO2 Max value stays at 45! 

Any recommendations?

(Maybe someone from Garmin Support is able to help???)

Philipshambrook gave you a perfectly sensible reply and a 45 VO2max makes sense with your pace. Your VO2max will not increase if your pace will not get quicker and / or your HR will get slower.