I've noticed there are quite a few people with the problem of their text messages going thru on the Galaxy S4. I have been dealing with these issues for months now. I'm locked in a contract, so obviously I can't change phones or companies for that matter, without having to pay that outlandish early termination fee per phone.
My husband and I both have the Galaxy S4. I've had my phone for a little over a year, and my husband about 6mo now. The texts are spastic when they decide to go thru. I'd say about 50% of my texts send or even receive. I only know i have texts half the time when I reset my phone, which I do about once an hour so that I don't miss any important texts. Half the time I get texts that do decide to go thru, they show as me having to download the contents and those messages expire and half the time I don't get to see those messages because they decide to load after they expire.
I have had my phone replaced, the SIM card replaced 2 times now. I've used the stock messaging app, and tried 3rd party texting applications. I've tried soft resets, hard resets, deleting all messages, deleting the cache and running in safe mode. NOTHING fixes this problem. I've been in contact with several different tech support, specialty support, been to the stores. You name it, apart from a different phone, I've tried it.
My daughter has a iPhone 5c, and she has no problems with her phone. She can be sitting right next to me. We can send the same message at the same time to the same person and hers will go thru, and mine either takes 2-3 minutes to go thru, or it doesn't go thru at all.
I've had it. I have 3 of my 5 contracts ending at the end of this year and I've been seriously considering going with another service provider. I've been with Verizon for over 10 years now, and between the high costs and the lack of customer support when it's needed, I just can't seem to fathom keeping the contract anymore. There used to be perks for people with long standing contracts, but apparently that means nothing to them anymore. There used to be great customer service and support, but that hasn't been viable for years now.
And OBVIOUSLY Verizon trying to work with me, offering me a different phone out of contract, credits or anything other than making me reset the phone over and over and over and trying this and trying that, over and over.... is obviously unheard of!!