This error is pretty common and you can get it from various reasons. I will put below examples as they come to my attention. Watch this thread closely.

Because of the UPPER BOUND value:

gz@aix:/ # chfs -a size=+1G /locate/database35
0516-404 allocp: This system cannot fulfill the allocation request.
        There are not enough free partitions or not enough physical volumes
        to keep strictness and satisfy allocation requests.  The command
        should be retried with different allocation characteristics.

gz@aix:/ # lslv 10_lv069
LOGICAL VOLUME:     10_lv069               VOLUME GROUP:   vg10
LV IDENTIFIER:      00c2894e00004c000000010674bd4833.36 PERMISSION:     read/write
VG STATE:           active/complete        LV STATE:       opened/syncd
TYPE:               jfs2                   WRITE VERIFY:   off
MAX LPs:            512                    PP SIZE:        128 megabyte(s)
COPIES:             1                      SCHED POLICY:   parallel
LPs:                16                     PPs:            16
STALE PPs:          0                      BB POLICY:      relocatable
INTER-POLICY:       minimum                RELOCATABLE:    yes
INTRA-POLICY:       middle                 [color=red]UPPER BOUND:    1[/color]
MOUNT POINT:        /locate/database35 LABEL:          /locate/database35
MIRROR WRITE CONSISTENCY: on/ACTIVE
EACH LP COPY ON A SEPARATE PV ?: yes (superstrict)
Serialize IO ?:     NO
DEVICESUBTYPE : DS_LVZ

The Upper Bound is 1 and your data is spread on one disk only:

SUPSID01@root:/ # lslv -l 10_lv069
10_lv069:/locate/database35
PV                COPIES        IN BAND       DISTRIBUTION
hdisk122          016:000:000   6%            002:001:002:002:009

In this situation, you cannot increase the LV if the targeted size will spread on more disks than the UPPER BOUND value. So you have to change it with the chlv command:

gz@aix:/ # chlv -u 1024 10_lv069

gz@aix:/ # lslv 10_lv069
LOGICAL VOLUME:     10_lv069               VOLUME GROUP:   vg10
LV IDENTIFIER:      00c2894e00004c000000010674bd4833.36 PERMISSION:     read/write
VG STATE:           active/complete        LV STATE:       opened/syncd
TYPE:               jfs2                   WRITE VERIFY:   off
MAX LPs:            512                    PP SIZE:        128 megabyte(s)
COPIES:             1                      SCHED POLICY:   parallel
LPs:                178                    PPs:            178
STALE PPs:          0                      BB POLICY:      relocatable
INTER-POLICY:       minimum                RELOCATABLE:    yes
INTRA-POLICY:       middle                 [color=green]UPPER BOUND:    1024[/color]
MOUNT POINT:        /locate/database35 LABEL:          /locate/database35
MIRROR WRITE CONSISTENCY: on/ACTIVE
EACH LP COPY ON A SEPARATE PV ?: yes (superstrict)
Serialize IO ?:     NO
DEVICESUBTYPE : DS_LVZ

SUPSID01@root:/ # chfs -a size=+9G /locate/database35
SUPSID01@root:/ # df -g /locate/database35
Filesystem    GB blocks      Free %Used    Iused %Iused Mounted on
/dev/10_lv069     31.25     31.24    1%        4     1% /locate/database35