I would try using the latest development version of Dolphin and see if that makes any difference as well as trying out different sensor bar placements. It is also possible you are too close or too far away for the tracking to work properly. Sometimes things like lighting can also impact tracking.
Thanks for your reply.
Luckily enough, there was a far simpler (?) explanation, one that should remind me (and anyone else experiencing issues) to never ever take anything for granted.
Turns out - and of course I did *not* know that - the WiiU works a little bit differently than the Wii regarding the sensor bar. That is, assuming there's nothing wrong with my WiiU.

But here I'll explain what's going on with mine.
WiiU actually has the sensor bar turned off by default when there are no wiimotes synced with the console.
Yet, for a brief seconds (when you turn on the console, or you enter the setup app) the sensor bar is being turned on! That's why sometimes it happened to me that the pointer started working on Dolphin, only to stop after a few seconds.
I discovered all of this almost by chance: I wanted to make sure the bar was actually working so I took my smartphone camera (as you probably know, you can see IR leds this way) and looked at the bar with the WiiU already powered on... and I was a bit shocked when I saw that, well, no led was actually on. Then I synced a wiimote with the console and BAM!, sensor bar activated.
Mindblowing considering that I was under the assumption that, like the Wii, the sensor bar was always on. But as I said, it's probably NOT a good idea to assume something, only to find out things are actually quite different.