Please have a look here:
Maybe it helps you too.
Is domain.tld, the same domainname as the domainname in your full hostname? (Your maindomain)
Which Linux distribution do you use and what are your MySQL and PHP versions?
Do you find any errors within the RoundCube log files?
I also have to say that i host a lot of different domains on my server and clients are using RoundCube, IlohaMail or Uebimiau without any problems.
I had some problems as you described indeed, but that was with the RoundCube package provided by ISPConfig.
Since i use RoundCube Beta2, which is setup according my "within 10 steps" howto, i do not have problems anymore. It was the reason for me to use it on my own website.
The only thing, i do not like is that everytime i login for the first time, i have to remove @www within the e-mailaddress. But that is no big problem at all.