In fact, this was not at web interface level, but at git command line level.

I have to repeat a simple git push commands several times (up to 10 times), until the communication is accepted, and the source code change is stored on the server...
Pretty disappointing for a source code hosting service...
Thanks to god, git is a distributed source code management system, so I can keep the commits on my side until their server is up...

Self hosting with our little fossil tool, in addition to using public hosting sites as mirror, sounded like the right approach.
By experiment, I do not trust outside services for storing my most precious data, even more if the data - and the hosting service - are free.
Using fossil on our web server is free, fast, safe, and in fact, full of features.

Update:
As reported by Martin, there is a DDOS attack going on, maybe this is the reason why this is not available...