I'm sorry to hear about any trouble sending messages! Let's get this back up and running for you. Is this happening on iMessages (blue) or SMS (green)? All contacts or just one? Which zip code are you in? Please give this a try as well: http://vz.to/1br15Eg
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WiFi will not be connected unless you are having access to it.
Although there is free WiFi it does not stay connected all the time outside your home network.
Make sure the send as text/SMS/MMS is on.
Make sure that is set to on even if on WiFi.
You can check out other settings and help from the Apple Forum.