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Yes, the messaging system has not been working reliably for a while now, both sending and receiving. If you are on the new messaging system, you can use the old interface in conjunction as it is more reliable.
For jobs that are time sensitive, I now ask clients for a preferred reliable way to contact them for immediate response (email). But of course Upwork's messaging system is the best platform to use for your safety and in case of disputes etc. I send an email to make the client aware but also deliver everything through oDesk for records.
Until the system is fixed, and generally for quick turn around projects.