Thank you both for the reply.
Unfortunately I have no access to a scope
I just changed the modem I have connected to another one (I have two of them). I also removed accidently removed the GND connection between the TXB0104 and the FT232 cable.
Turns out that it is now much more stable. I actually get a lot of characters thru correctly. Probably around 75% of them.
Of course this is still very bad for reliable communication...
Another interesting find I did when replacing HyperTerminal with RealTerm is that the CTS line from the modem is blinking a lot.
I am very novice at this but this makes me think that there is either a lot of noice, or that actually the TXB0104 have trouble knowing which direction it is going to send data and hence flips back and forth.
Then I wonder why this can be, if it is like that. It would actually work great with another chip that does snot have auto direction. I just need 2 pins in each direction.
Is there such a chip to recommend?