perldoc Storable says:

CODE REFERENCES
       Since Storable version 2.05, CODE references may be seri-
       alized with the help of B::Deparse. To enable this fea-
       ture, set $Storable::Deparse to a true value. To enable
       deserializazion, $Storable::Eval should be set to a true
       value. Be aware that deserialization is done through
       "eval", which is dangerous if the Storable file contains
       malicious data. You can set $Storable::Eval to a subrou-
       tine reference which would be used instead of "eval". See
       below for an example using a Safe compartment for deseri-
       alization of CODE references.

       If $Storable::Deparse and/or $Storable::Eval are set to
       false values, then the value of $Storable::forgive_me (see
       below) is respected while serializing and deserializing.
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Perhaps you need to set that correctly on both ends, when using POE::Filter::Reference with Storable.