I could move the files, but since I absolutely need them to be in .shp, I'll have to re-export everything. I'll try and if it's a workaround I'll do it, but it's still a pain in the *ss...
Thanks for the link Hasdrubal.
The final post ended like this:
Does this mean that there is a 128 character limit to the path for a shapefile? Well, I tried and it seems to be right.
I already had 120 characters in my path's name (it's very standardized...) so I created a shp with a short name (abc.shp) for a total of 127 characters. Tried adding fields and it worked. I created another one with a lot more characters (abcdefghijklmnopqrstuvwxyz.shp) so... well a lot more than 128. Adding and deleting fields worked.
When I created another with a short name (a.shp), it didn't cause any problem but when I created a new one with a long name (abcdefghijklm.shp), I couldn't add any fields or deleting any in my first one with the long name.
So, it appears that Arc is reading the first 128 characters and if after that, there's more that one file with the same first 128 characters, it can't modify it because it can't find the right one...
It's kind of like in the old times, when Dos had 8 char file names... myshap~1.shp ...
But, (because there's always a but), that problem's not happening on one of my colleague's computer.
I don't understand why such problem should occurs in a software worthing more than my annual salary...