I just accessed Message+ via the website, after logging in to My Verizon and selecting Send a Message from Plans & Services (https://web.vma.vzw.com/vma/webs2/Message.do ) and connected fine. Using IE, MS Edge, FireFox and Chrome browsers, they all connected but only showed two most recent message strings. The website access is NOT in sync with the desktop app nor the phone, tablet app in showing message strings. This doesn't sound like your issue but is an issue and could be related.
Are you using your profile login or phone number login to access the website? I don't think it should be any different but might be. Also, which browsers have you tried?
Having multiple ways to access your messages is very important and convenient. We want each of those ways to work seamlessly for you. Let's figure out what's going on when you try using Verizon Messages via the website. So that we can help, please clarify what you mean when you say, "Verizon messages is not connecting on desktop"? Are you receiving an error message? If so, please let us know what the error says. Also, what browser are you using? When did you begin having trouble accessing Verizon Messages via the website?
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Thank you for verifying that. What type of computer are you using to complete the messages?
Follow us on TWITTER @VZWSupport If my response answered your question please click the Correct Answer button under my response. This ensures others can benefit from our conversation. Thanks in advance for your help with this!