Hi guys (and gals?

)
Hi.
So here's what I'm Wondering;
After a transaction is made, is there any chance it won't be confirmed at all?
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Yes.
If so, what would cause it not to be
- Insufficient fee
- invalid transaction
- poorly connected wallet
and what are the odds of that?
- Nearly zero if you pay a sufficient transaction fee
- Nearly zero if you use well written and reviewed open source wallet software
- Very, very low as long as you can access pretty much everything else on the internet
If there's a re-org and the transaction goes back into the mem-pool, would it be confirmed automatically later?
Almost certainly. That's WHY it went back in the mem-pool instead of being deleted. However, in MOST cases, it will already be confirmed in the re-org.
Also, what was the longest period of time you had to wait for a confirmation?
Three weeks, because I INTENTIONALLY paid an insufficient transaction fee. I was not in a hurry, and just kept re-broadcasting the transaction until transaction fee requirements dropped.
I once made a transaction that took almost a day for it to be confirmed, and if I remember right it also took a long time until it even appeared in the recipient's wallet. could it have been the result of a bad wallet?
Depends on the wallet you and the recipient were using. Perhaps they were using a wallet that only displayed CONFIRMED transactions? Perhaps you were using a wallet that did a poor job of fee estimation? It's also possible that the required fee for a fast confirmation suddenly increased immediately AFTER you sent the transaction. This is why I like to use wallets that support RBF.
It was about a year ago so I don't think the network was very busy.
Or, maybe it was.