Here are a few cases where Tweets will fail:
Length of message:
This issue is most commonly caused by the length of the prepopulated Twitter message within your widget. Keep in mind that there will be a referral link appended to the end of your Tweet, which may cause the message to go over Twitter's character limit of 140. As a best practice, keep your message to 110 characters or less. If you're using HTML code for symbols (e.g. & for an ampersand), include the extra characters in your count.
Using your own Twitter App:
Please make sure your Twitter app is set to the following conditions: App > Settings > Read, Write and Access direct messages