I started receiving incoming text messages with long delays about a month ago, shortly after moving to a new town (from North Brunswick, NJ to New Providence, NJ). Never had this problem before then, and I also didn't update the OS around that time. The phone is an iPhone 5s, running iOS 9.1 at the time.
My SIM is from ekit, a reseller that puts me on T-Mobile or AT&T, depending on what has a good signal. It seems to prefer T-Mobile.
I tried rebooting the phone, but that didn't help. I did not try resetting anything.
Yesterday I updated the OS to 9.2 (which included a "carrier update"). Received another couple of delayed texts a few hours after the upgrade; they had been sent more than 48 hours earlier.
I'm now getting a T-Mobile SIM, pay-as-you-go from T-Mobile themselves, no reseller this time. It seems unlikely to me that the phone or the OS are at fault, since the problem never happened before I moved, became quite frequent after the move, and I didn't do anything to the phone around the time of the move. I tentatively blame ekit, but I must confess I don't know how these resellers operate and what part they play in the actual delivery of text messages. Since they charge me per text, they're obviously in the loop somewhere. I contacted their customer service and they said there weren't any errors in my service log, but then again, I suspect that a delayed text isn't considered an error, so that doesn't help much.
I'll post again to report on whether or not the problem goes away after I switch.
UPDATE: I should have mentioned that I only seem to be having trouble receiving texts; as far as I know, the ones I send still arrive promptly.