I’ve recently learned that some citations to ASCL (and arXiv) entries are not caught by ADS because some BibTeX styles (.bst) don’t support the eprint field, which ADS uses when generating the BibTeX for ASCL and arXiv entries. The lack of support for the eprint field results in a citation that formats the ascl ID incorrectly; for ADS to be able to find and count the citation, the ascl ID needs to be formatted just as it appears in the code entry, e.g. ascl:1010.051 for NEMO. The arXiv site has a list of BibTeX styles that have been updated to support the eprint field, and Norman Gray’s nice urlbst code can add this functionality to existing .bst files.
(This information has been added to the Citing ASCL code entries page.)