MMS/Group Text Trouble After Multiple Texts

[Auriana]

I'm not sure if this is a Samsing issue or a Verizon issue. It has happened on all my Samsung phones over some years now and I am still baffled. I have a number of group texts and when there are a lot of texts in a short period of time, all of the sudden it stops me from sending or receiving the texts. I get the skinny thing followed by a cannot send error when I try to send one and incoming texts show up under texts from individual contacts as messages to download. However, it won't let me download them. This continues for a period of time before everything is restored to normal.

My husband has had the same phones as me on the same plan and never had this issue. I've been searching forever for an answer.