This is a very common capoeira movement and I've seen similar things in some kung-fu styles.
I can do it for a couple of seconds (or 2,3 steps) for about two years now, but never managed to go past this barrier. Does anyone have tips ?
Yeah Thats it! Good workout!
From what you describe, it sounds like the problem you have is maintaining your balance using other parts of your body other than your arms. While your arms and hands will bear the weight while in a handstand, you should also focus on using your core strength (abs and back) to hold yourself up. The idea is similar to standing up straight on your feet and using your core to maintain an upright posture (otherwise you slouch). The concept is flipped upside-down for a handstand. Having strong arms will not help much if the the rest of your body is tipping over.
While you can improve your arm and wrist strength (it will help), you should also focus on doing exercises to strengthen your abdominal and back muscles. There are many, many different types of strength exercises you can perform to improve your core. Some of these include:
Those suggestions aren't a training regimen necessarily (you didn't mention any details of what your current training or physicality is). You can decide for yourself what you think is appropriate for your body and fitness level.
In terms of addressing balance, you can try doing a handstand but with your feet and legs separated (like going outwards in a center split). This is actually something I learned from juggling. The purpose of doing this is to spread your weight over a distributed area rather than keeping it concentrated in a smaller space. It will force your body to figure out which way to move and and train your muscles to realign your center of mass so that you don't lose balance. Once you start getting used to that feeling, you can slowly move your feet and legs closer together. The movements you make to correct your balance will become smaller and more subtle as you bring the weight into the middle.