Intensity minutes not adding up from activities ?

Go to garmin connect, tap on the watch icon on top of the app, user settings, heart rate zones and check how they are set up. You can also reset and see if that helps. Make sure to sync the watch after you apply any changes

Please share a weblink to the activity where you believe the Intensity Minutes were not correctly calculated, so that we have a look. Please note that in order to earn intensity minutes credit, you must reach or exceed 10 consecutive minutes where your heart rate is elevated above the threshold that is considered moderate intensity. So if the effort was frequently interrupted, and there were only shorter bursts (<10min) in the upper HR zones, then they won't count.

Thanks for your suggestions, that's done (heart rate zone setting is % of max rate), synchronized, reset done. Problem persisted.

As I wrote: please share a weblink to the activity where you believe the Intensity Minutes were not correctly calculated, so that we can have a look at it, and tell you what could be wrong. 

Hello trux, thanks for your answer. The typical activity has some 20 to 40 minutes in each zone. I give here a link example activity done earlier today.

Result after synchronizing is unforeseen in that I see  now 11 (eleven) intensity minutes in connect app for today while time spent in zone 4 was 29 min and in zone 3 for 12min45s according to the activity. Hmmm.... better than no counting at all but still room for improvement.

Another observation : while saving  the accomplished activity on the watch, a short 'failed' message was displayed on the watch. Anyhow, it would proceed and display as usual, and upload to connect app did work as well.

Indeed, the HR graph shows 25 consecuitve minutes in the Z4, so that should be sufficient for some IMs.

Another observation : while saving  the accomplished activity on the watch, a short 'failed' message was displayed on the watch.

That may be the reason. Verify how much free space is remaining on the device storage (over the USB cable). Delete old activities from the folder //GARMIN/Activity, and also unneeded workouts and courses.

...thanks  trux,I will try to free up space on the watch and tell here what happens.

But why is the daily Resting Heart Rate in the equation ? The available documentation explains that % of Max Heart Rate is the criteria, and that is exactly what I need when I wear the watch only during my activities and not during my office hours or at night. If there is any more knowledge about how exactly the watch operates it would be interesting.

The available documentation explains that % of Max Heart Rate is the criteria

No, the available documentation (for example the document How Does the Intensity Minutes Feature Work on My Garmin Watch?) tell this:

"Most devices with wrist-based heart rate senors will calculate intensity minutes by comparing your current heart rate to your average resting heart rate"

So if you wear the watch for activities only, you will never have accurate IM. The Resting HR is used also for other features of the watch, so the lack of it will influence also other functionality, including possibly also the Calories calculation.

This started to happen to me a couple of weeks ago. 

I used to gain a lot of Moderate Intensity minutes throughout the week from daily walking, and manual work, now I only ever seem to gain Vigorous Intensity minutes when I go running. 

I also find the heart rate monitor okay for running, but for anything else, it performs poorly. I can be out of breathe, sweating and My heart can be beating through my chest, and I will look at the heart rate graph and its only in the 80's.