With a normal jfs filesystem, the maximum size is 2GB. Sometimes users have a ulimit value set which puts a limit of 1GB on the size of files they can create (the value is in 512byte blocks so it can look like 2GB when it's really 1).
You can create a jfs filesystem to be large file enabled which allows files up to (I think) 64GB. This is fine, but large-file enabled filesystems have poorer performance if they contain lots of small files so don't create them unless you need them.
The solution, if you are using AIX 5L (5.1 or 5.2) is to use JFS2. Enable the 64 bit kernel (not required, but improved JFS2 performance). JFS2 has a maximum file size of at least 1TB; I think the theoretical limit is substantially higher. If you need an individual file to be larger than 1TB, you probably ought to have a think about whether you're doing things the right way