The important point regarding ACA-1362 airworthiness certificates is whether there is any supporting documentation that a non-expiring one was ever issued. If you check the FAA records for both of my Cadets, N34782 and N29392, you’ll see that the most recent ACA-305a Annual Inspection Reports show expiration dates in section 4, line F that are one year after the date of the inspection. Both of these planes were actually issued the modified C of A’s at the time of those inspections. You’ll find links for those records on the culvercadet.com website. The file for N34782 contains scanned images of both the old and replacement C of A's. Those documents only entered the file after I exchanged my old one for the new version. The FAA Inspector mailed the old one and a copy of the new one to Oklahoma City.
Fortunately, even though the last Annual Inspection Reports indicated otherwise, I had the C of A’s for both of these planes with the non-expiring wording on them. Had I not possessed those modified C of A’s, there would have been no evidence that they had ever existed.
The form ACA-305a for Culver N34855 is an example of the form being correctly filled out when the modified C of A was issued.
The bottom line is this; If your C of A is missing, check the FAA airworthiness file to see what the most recent form ACA-305a says. If it indicates that a continuous C of A was issued, you can make your case with the FSDO for issuing a replacement. If there is a logbook entry stating that a continuous C of A was issued, that might work too.