Burner ap or burner phone?
After carrying around two phones for many years, maybe three,
I finally switched to using a burner ap on my smart phone a few years ago.
None of these text apps have been dependable .
Past month at least, I don’t get texts when out of WiFi area.
And they don’t pop up later either.
Any suggestions or helpful hints?
No opinion on burner app or phone.
But for your not getting messages while outside of wifi range...
There is probably a setting on your phone, something like "Use cellular data". It may be that is a universal setting, or it might be set per app, or all in one place, per app...
It may have been set to use cellular data at one point, and an update etc may have changed the setting "for you".
Anyway, look for something like that, it sounds like that is probably the culprit.
I use “Burner” app on my phone. I’ve had pretty good luck with it. Had it for 2-3 years now, I think.