After pressing deliver you should be able to see whether all the files you attached are still attached when it shows them on the order page. Though it can sometimes not be that easy to see which is missing since it only shows the first so many characters (around 7 or 8?) of the file name.
I don’t think they should deliver the same file 3 different times unless they can see that it didn’t go through the first 2 times - otherwise you still have the risk that the latest delivery will be missing an attachment.
I think the best idea is to deliver with a link/links to somewhere like dropbox in the delivery box. And also try to add attachments too (especially if they’re small like you said). The person delivering could also say that if that all the files are on the links below if any of the files attached to Fiverr are missing - or better wording.
Also, for big files, somewhere like dropbox is better than Fiverr because if 1 out out of multiple files didn’t get uploaded you only need to re-upload that one file instead of uploading all the files again on Fiverr as attachments (and I think if you have the software version of dropbox you could start an upload from where it left of if it stopped uploading for some reason (such as connection problem)).
Also, one of the options for buyers after a delivery is now something like “a partial delivery was delivered” if you say you’re not ready to accept an order. So it will be easier/faster for Fiverr to see if a partial order was delivered (instead of just asking them to deliver any missing file(s) in a revision). Even if the cause of it was due to a bug or something with Fiverr’s attachment feature - which they’ve already been notified of and there’s threads about it.