I suspect its fucked. SMART is likely reporting lots of write errors. In linux you can see these in dmesg command. It will also give a reason for the remount as RO. Find a SMART disk tester and run a test on it.
Discussion
Ok, it holded now ome hour without. But before it always did.
I will look into dmessages tomorrow. What is a smart disk Tester?
SMART is the disks internal tests to determine it's own health. It's also what is likely making its read only. You can get software to read this smart data, it gives you a clue about the drive health. With it being external, try changing the USB cable.
Thank You.. I already changed the USB cable. How do I Access this data on Linux? I will check what fsck will tell me, later. At the Moment I copy down the Data, but it is still on rw mode. Since about 2 hours.