Some tweets which mention your Twitter account are not creating tickets, but others are successful. Why would only select tweets not create a ticket?
If most tickets using mentions are flowing in from Twitter, it is likely that your account is authenticated correctly, but the account's Twitter settings could very possibly be overriding the retrieval of those tweets. Before becoming too alarmed, please check on the mute and blocked settings within Twitter to confirm someone did not block certain words contained in the missing tweets or that those tweets did not come from a muted or blocked user.
To find these settings, someone with access to the Twitter account will have to visit the Twitter Settings and privacy page and look through these settings in the left sidebar:
Changing these settings may not retroactively retrieve blocked or muted tweets, but the settings change should cause future tickets to successfully create tickets.