I have been using FastMail since a long time now and inbox is getting bigger than 20GB and will soon reach a limit of 30GB. I gathered all emails from GMail, Yahoo, Apple etc. using IMAP into FastMail account and it is so good to have all emails in one account. But, as emails are too many it was good to archive some old emails to save space.
My solution for this was to search and archive (send to archive folder) emails I do not need on FastMail and sync them using IMAP to Mail App on Mac OSX. After setting up my FastMail IMAP account on Mail App, I can use it on daily basis also and took a backup of Archive folder into Dropbox and cleaned the Archive folder from FastMail. As Mail App exports is as MBOX format, I could easily open the MBOX again on the Mail App to access the emails. Love the solution for now. This way I can archive and backup all my important emails and cleanup space without deleting them.