We haven’t been told that Fiverr will suspend accounts for that reason as far as I know. It will affect your level. If you were a level 0 it will stop you from being promoted to level 1 at evaluation time if it’s < 90% at that time, and if you were >= level 1 at the time of the evaluation it would mean you’d drop a level.
What you can do is change the gig set up to give yourself a higher number of days to deliver and/or change the “limit orders in the queue figure” figure for gigs or pause gigs when you won’t have time to work on new orders for them or turn on out of office mode (though that won’t stop past buyers from buying). Or when you send offers give a higher number of days delivery than you normally would for that gig/package/task.
edit: It does say this in the TOS:
Sellers who cannot maintain their high quality service, experience a severe drop in ratings, or stop delivering on time risk losing their Seller status and the benefits that come with it. For example, late deliveries, warnings to the Seller’s account and cancellations can cause a Seller to move to a different Level.