Has anyone seen an ASA not record hit against an ACL? I have two 5520s in a Primary/Secondary configuration, versions 8.4(1) and ASDM 6.4(1). There are several ACLs that are all recording zero hits but I know for a fact that those are what are matching for them to get out.
Could you verify if you are able to see the hit count from the CLI, by doing "show access-list". This could be an issue with the ASDM itself, it may not able to calculate the MD5 hash value for the ACL.
Could youm also tell me if those particular ACL's contain any network object for protocol???