Thank you for your reply Mariana, but I think I found the source of the problem. It seems to be my phone that is causing the issue. Last night I decided to pop the SIM card into an older phone and within moments, a flood of texts started to come in.
I'm still not sure why the phone is the source of the problem and why it happens sporatically every so often, but I'm going to keep the SIM card in my old phone for now until I can figure it out.