Did you ever got the following on chfs command?

"[u]0516-1407 lextendlv Reboot with the 64-bit kernel and try again.[/u]"

aix@root:/ # df -g .
Filesystem    GB blocks      Free %Used    Iused %Iused Mounted on
/dev/lv_data   1024.00     27.02   98%       51     1% /home/data
aix@root:/ # chfs -a size=+1G .
[color=red]0516-1407 lextendlv Reboot with the 64-bit kernel and try again.
0516-788 extendlv: Unable to extend logical volume.[/color]

This can happen if you want to extend the filesystem beyond 1024G and you have 32 bits kernel. For that you need 64 bits kernel. In my situation, for whatever reason, 32 bits kernel was running on 64 bits processor:

aix@root:/ # prtconf | grep bit
CPU Type: 64-bit
Kernel Type: 32-bit
aix@root:/ # bootinfo -y
64
aix@root:/ # bootinfo -K
32
aix@root:/ # ls -l /unix
lrwxrwxrwx    1 root     system           21 Feb 07 2010  /unix -> /usr/lib/boot/unix_mp
aix@root:/ # ls -la /usr/lib/boot/unix_*
-r-xr-xr-x    1 root     system     15397949 Jan 29 2010  /usr/lib/boot/unix_64
-r-xr-xr-x    1 root     system     12531275 Jan 29 2010  /usr/lib/boot/unix_mp

For your information:

/usr/lib/boot/unix_64 = 64 bit multiprocessor kernel

/usr/lib/boot/unix_mp = 32 bit multiprocessor kernel

/usr/lib/boot/unix_up = 32 bit uniprocessor kenrel

In this situation, I had to do the following:

aix@root:/ # ln -sf /usr/lib/boot/unix_64 /unix
aix@root:/ # ln -sf /usr/lib/boot/unix_64 /usr/lib/boot/unix
aix@root:/ # lslv -m hd5
aix@root:/ # bosboot -ad /dev/ipldevice
aix@root:/ # shutdown -Fr
aix@root:/ # bootinfo -K (should give you now value 64)

In your situation, it depends. Maybe you have only 32 bits cpu or you don't have 64 bits kernel installed. Also you may have a reason why you are running 32 bits kernel: probably some application requirements.

One thing is for sure: if you want to extend the lv beyond 1024G, you need 64 bits kernel.