It seems to affect primarily iMessages when I'm out of data, or group texts, or other somehow unusual text messages - I mostly just never get them at all, but it's inconsistent. Sometimes with iMessage I'll get a slew of them (late) when I get on a wifi network after having been only on 4G for a while. Some group texts and regular SMS messages I know I have missed entirely and they never get delivered for whatever reason.
This quoted part pretty well says everything. This is an issue with your iPhone and using iMessage specifically. Part of the messages you aren't receiving are messages from other iPhone users that require a live data connection to receive while you don't have access to WiFi. No mobile data left on the account? No messages until you're on WiFi, no matter how much unlimited SMS message support you have. Simple as that.
One solution for that issue would be to
disable iMessage and force everything through standard SMS instead of using Apple's proprietary data-based messenger for these messages.
Unfortunately, that only addresses half of the problem. The other half is a combo issue between Apple and AT&T and has been present since iOS7. The way iOS is configured, if an AT&T network based SIM card is installed in an iPhone (and Airvoice is an AT&T MVNO), Apple disables the ability to manually configure MMS data settings. MMS handles most long SMS messages (over 160 characters) and all messages that have media attachments, and it requires access to a carrier specific data proxy portal to receive it. This means that unless Apple blesses support for your specific AT&T MVNO, they'll break basic functionality. They're ruining core usability for people who use providers they don't approve of. Consider it an Apple tax. You want your phone well supported? You're going to have to pay extra for a provider they bless, or suffer with far less network coverage using a sub-par network (say, T-Mobile). Don't blame Airvoice, blame the manufacturer of your phone and AT&T. This is only one of many reasons why I recommend against iPhones in the first place. The only way to circumvent this issue and manually configure MMS settings on a non-blessed AT&T MVNO is to jailbreak, which has a whole raft full of problems that comes with doing it.
If you want AT&T coverage with an "unlimited" talk and text plan that supports MMS, you're going to have to go with AT&T GoPhone or Cricket (both owned by AT&T and they're undercutting their own wholesale customers like Airvoice on data prices to put them out of business and increase direct revenue with Cricket) and pay nearly twice as much as you're paying now unless you can sucker others into making a deal with the proverbial devil with you, StraightTalk Wireless BYOD (owned by America Movil and the customer support is terrible) where you'll pay
more than twice the price you are currently, or Consumer Cellular which is a perfectly fine postpaid MVNO that's in
the guide, but you have to actually pay for what you use instead of getting the promise of "unlimited" talk and text, and you're unlikely to get away for anything less than $35/month if you need anything approaching those sorts of "unlimited" usage numbers - Consumer Cellular is the most cost effective when you're dealing with multiple lines, not a single user.
Now, if you can manage T-Mobile coverage without roaming in your area, there's an alternative. T-Mobile and T-Mobile MVNO SIM cards don't block manual data and MMS configuration under iOS like AT&T SIM cards do. This opens up Ting (postpaid pay for what you use - not cheap for just one line for the same reasons Consumer Cellular isn't cheap for one phone) and Ultra Mobile. Ultra's terms and conditions still tweak me a little, but since the loss of P'tel, they're about the only T-Mobile MVNO left that has similar plan pricing and structures for the "unlimited" talk and text users. Fortunately, they have proven to at least be a reasonably long-term viable MVNO, which again doesn't mean much anymore since the major carriers started undercutting their wholesale customers on data prices with their own "boutique" MVNO brands (Cricket, Metro PCS, Boost Mobile) and P'tel went under from the squeeze after being around for 15 years.
In your case, Ultra has a $19/month "unlimited" talk and text plan with 100MB of LTE data. That should work out for you to fix the issues you have with your iPhone and Airvoice without replacing your handset provided T-Mobile coverage without roaming works for you. If you need AT&T coverage and the $20 Airvoice plan works for you, you'll just need to ditch the iPhone and switch to Android or Windows Mobile if you want a smartphone with proper SMS/MMS support.
