Until you need to update it to cope with Y2K or Y2K38 or GDPR or some other external factor...
There’s going to be some point where you’ll be glad to have original specs and docs and source code on hand (along with a good COBOL dev) so you don’t have to decompile and reverse engineer the damn thing. (Which IIRC had to be done for a relatively large percentage of COBOL-era systems updated for Y2K.)