The most likely explanation is that you were trying to send a large email simultaneously to a significant number of recipients. Test, first, sending it to a single recipient to verify my theory. Then, if that succeeds, send to just a few recipients at a time, spacing them out with an hour's gap between.
Usually, people will only reach the hourly sending limit on trial accounts (where the limit is 125 MB per hour and 250 MB her day). For other kinds of accounts, see
Limits on sending/receiving email in
https://www.fastmail.com/help/account/limits.html