My Dell Venue used to auto synch messages, it doesn't now. I have to open the application and they will synchronize.
What messages? Email? Text? And what application?
First, try clearing the app cache for whatever app you are using for these messages. If that doesn't work, perhaps uninstalling and reinstalling the app will get the messages syncing again. If it's email messages, deleting and then re-adding the email address may work.
I assumed the forum was for Verizon Message+ that is what doesn't autosynch. I have deleted the app and data.
Have you double-checked your settings to ensure that syncing for the various apps is still turned on? If you have a Master Sync toggle, have you ensured that it's on?