Hi SandraI,
- We would be happy if you purchase our tickets from SBB directly 
That's my preference as well. Unfortunately, SBB payment service isn't too gentle with cashback/rewards-type credit cards :(.
- I recommend you to download our SBB Mobile App and try it once again. It should normally work with foreign credit cards as well.
I did that as a workaround that I read from a thread here regarding "Payment authorization rejected". Unfortunately, that didn't work either. Interestingly enough, the same credit card works on SNCF, OBB, CD.CZ without any issue. I always prefer to book directly with the train operator but in this particular instance, it unfortunately has proven quite frustrating to place a booking.