Thank you for responding to my question.
Message+ is a Verizon product which synchronizes and stores messages across different platforms. The desktop version is being used which is downloaded from the Verizon web site. You can find out more about it at http://www.verizonwireless.com/support/terms/products/verizon-messages.html
The message log is where messages are stored for display on the desktop.
The Jetpack in question is a model MiFi 5510L and it is running software version 1.34.23.
Aside from silently dropping long messages, the Jetpack's performance is flawless. It displays whatever text is sent to it. No attempt is being made to send a picture message to the Jetpack.
The messages are purely being sent from other cellphones via Verizon's cellular network. There is no Wifi being used.
There are no e--mail or web apps being used.
Alright that's a new service for me. Didn't realize people would ever depend on a Jetpack to receive text or picture messages.
This may not have anything to do with the Jetpack and may be something VZW needs to investigate for you. I'll check around and see if I can dig up anything else to assist you.
The display on the Jetpack is single bit depth, so I never thought that it would display picture messages in and of itself. It's only suitable for icons and messages, which is fine.
In addition to 4G access (which it performs superbly), the Jetpack is being used to store automatically generated status messages for later review.
I have since researched the problem further and believe that the problem is with the Message+ desktop application itself. It has a number of problems which I have detailed in another post. See Re: Has anyone used Verizon Messages Desktop App for further information.
Messages DO show up in the Integrated Messaging service web site, so that is an acceptable workaround.