Only when fans own their own servers, as the famous AO3 rallying cry goes and only as long as fans are willing to do the work of building and maintaining the archives that live on those servers, and interfacing with their users and with the press, and putting redundancy measures in place, and making policy decisions and recruiting fellow volunteers and all of the other responsibilities involved with running an archive will fan archives exist.
So while I don’t think that fan fiction is too large a genre to completely archive, I do fear that at some point, the preponderance of corporate owned social media may lull fans into thinking that they don’t have to appoint themselves archivists of their communities’ material. If fans stop volunteering to fulfill this important cultural role, then fan works will cease to be archived in a reliable way.