Our RFC user does not work; we always get the the error message "Invalid user or password". But we are sure that both are correct. What could be the reason?

This is probably an issue concerning uppercase/lowercase characters. GuiXT translates the given password to uppercase (unless you enclose it within "...."). 
This was appropriate for earlier SAP systems but later ones use case sensitive passwords.

I suggest you either use a password that consists of uppercase letters and digits only, or you put it into "...." in the profile. In the case of encrypted password (RfcpasswordEnc): create the encryption including the "...." and then put the result into the profile without enclosing the encrypted string within "...".

Please note: In order to encrypt a password "xxx" including the "..." characters, you need the MS DOS command

guixt rfcpassword  \"xxx\"

Without the backslash characters the "..." are not included into the encrypted password, since the MS DOS command interpreter treats "xxx" the same way as xxx.