When using the deprecated SMS/Messages resource URI to send text messages, messages with one or more non-GSM characters are limited to 70 characters. Any SMS messages that include 1 or more non-GSM characters will be separated by Twilio into messages of 70 characters or less. You can find out what characters are included in the GSM set here. You can also paste the text you're attempting to send on a third-party checker to verify your messages are free of non-GSM characters. Here is an example link that works as of fall 2015.
If you are sending unicode messages to mobile numbers in US and Canada, try the Messages Resource URI instead. You can send messages containing up to 1,600 characters without being split. Check out the FAQ Does Twilio support concatenated SMS messages or messages over 160 characters? to learn more.