I'd suggest that you add a few lines just before the mod script "exits". I'm aware that mod_perl script don't exit, but I mean at a convenient point after the html request that caused it to be invoked has completed (to avoid impacting your users). I can't be more precise about it as I know naff all about mod_perl.

Something like this:

...
use Devel::Size qw[ total_size ];
...
unless( int( time ) % 3600 ) {
    open my $sizelog, '>', '/some/path/' . localtime() . '.log' or war
+n $!;

    print $sizelog "$_ =>", total_size( $::{ $_ } ) for sort keys %::;

    close $sizelog;
}
[download]

The idea is tha once per hour (assumes that you have a fairly steady flow of activeity on the site), that you dump the total sizes of every package known, to a time-named file. You'll get output that looks something like this:

 :> 378
☼ :> 418
↕ :> 262
▬ :> 345
↨ARNING_BITS :> 400
↑ :> 330
! :> 403
" :> 292
$ :> 272
+ :> 552
- :> 552
/ :> 382
0 :> 386
1 :> 425
2 :> 407
<none>:: :> 460
@ :> 950
ARGV :> 390
Devel::Size: Calculated sizes for compiled regexes are incompatible, a
+nd probably always will be
AutoLoader:: :> 25020
BEGIN :> 272
CORE:: :> 930
Carp:: :> 17283
Devel::Size: Calculated sizes for compiled regexes are incompatible, a
+nd probably always will be
Config:: :> 91676
DB:: :> 850
Devel::Size: Calculated sizes for compiled regexes are incompatible, a
+nd probably always will be
Devel:: :> 22891
Devel::Size: Calculated sizes for compiled regexes are incompatible, a
+nd probably always will be
DynaLoader:: :> 55547
ENV :> 6491
Devel::Size: Calculated sizes for compiled regexes are incompatible, a
+nd probably always will be
Exporter:: :> 23537
INC :> 1710
IO:: :> 928
Internals:: :> 3421
Mac:: :> 1725
PerlIO:: :> 2363
Regexp:: :> 933
SIG :> 3595
STDERR :> 274
STDIN :> 272
STDOUT :> 274
UNIVERSAL:: :> 1857
VMS:: :> 1248
Win32:: :> 11242
] :> 355
_ :> 345
_<..\perlio.c :> 336
_<..\universal.c :> 348
_<..\xsutils.c :> 340
_<.\win32.c :> 328
_<Size.c :> 339
_<c:/Perl/site/lib/auto/Devel/Size/Size.dll :> 479
_<dl_win32.c :> 330
_<perllib.c :> 328
attributes:: :> 947
Devel::Size: Calculated sizes for compiled regexes are incompatible, a
+nd probably always will be
main:: :> 299655
stderr :> 274
stdin :> 272
stdout :> 274
strict:: :> 6427
total_size :> 844
utf8:: :> 4344
Devel::Size: Calculated sizes for compiled regexes are incompatible, a
+nd probably always will be
vars:: :> 9566
warnings:: :> 58863
[download]

With luck that will prevent you from being overwhelmed with data (a smallish, easily compared file, once per hour), that should show you which package(s) are accumulating memory over time.

Once you have that information, you can then concentrate your efforts there.