I found it out myself... In case someone is interested:

1) install your stylesheet (see above) 2) Format/Edit Stylesheet 3) Click on your Stylesheet notebook file 4) Option Inspector/Notebook Options/File Options 5) Set Saveable on True

Now you can save your stylesheet notebook with File/Save after modifying styles. Remains the question why this is not the default setting...

Thanks David, I guess this works too. However, another problem is that, if you want to change another style in your personalised stylesheet, you need to save it again under another name. It is not possible to save the same file. For instance, if you want to modify a style in DefaultPerso.nb by going to Format / Edit Stylesheet and click on DefaultPerso.nb you can modify a style but you cannot save it because File / Save is greyed out. You can only save it under another name. So the modification is useless. It is only active during the actual session. It is lost when you close Mathematica and reopen it. This is really a nightmare. I like Mathematica a lot. It's the best for symbolic calculus. But the frontend comes from another age.
Another issue is the grouping of cells which would be very useful for notebooks with a lot of content. The problem here is if you insert a new cell within a group, it is broken up and you need to regroup it again. Also, if you want to move a group by cutting and pasting it elsewhere in the notebook it will be merged into the previous group, which is mostly not what one wants to do...

Thank you, Bruce, this works. I tried a similar approach: I opened Default.nb, saved it as DefaultPerso.nb and installed it as the stylesheet. But this doesnt work because it inherits the property "editable->false"... Wolfram should definitely make the use of stylesheets easier.