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So to summarize:
Fixing the past:
Try to get the late removed through polite friendly negotiation.
Safeguarding the future:
(a) Learn how to understand how CC "amounts owed" work in terms of FICO impact. The person who pointed out that you got into trouble because you thought there was an advantage to paying off most of your bill but not all of it is right. There's never a FICO advantage to that.
(b) Set up autopay.
(c) You can typically set up "alerts" on any credit card. I just picked one of mine at random and signed on. There was an option to make it tell me when a payment was due and another option to make it tell me when it was overdue. If you had chosen either (or both) you could have been automatically alerted well before they reported your card as delinquent.
This is one of those "oh darn" situations we can get into. Great suggestions in this thread. Hope you can "goodwill" the removal because it will follow you for a long time and effect your Fico Score. Also, lenders do not reach out it is your responsibility as a borrower to stay on top of your obligations (which I know you are well aware of). As was suggested, use alerts and at least minimum auto pay. For the very reason you got dinged I activated auto pay on everything and set alerts. The Fico Score hit is pretty harsh but it is.
This case is an excellent example of why it is a good idea to set up autopay for the minimum payment on all accounts. Especially if you travel a lot.