Skype enables communication using audio, video and text-based messages. Sometimes text messages, both SMS and traditional chat, won't transmit to their respective users. This can be for a number of reasons, some of which are beyond your control. Such issues can prove frustrating, especially when you use Skype for business and you can't send time-sensitive information.
Skype cannot send messages to offline users. It instead stores those unsent messages and deliver them once the user logs on. You'll know a message has been stored for delivery when you see a spinning icon of a ring next to it.
You may not have noticed, but your system may have lost Internet connectivity. Skype won't always detect this immediately, so everything else will appear to be functioning normally. If you've lost connectivity, try restarting your router and reconnect to Skype.
Insufficient Skype Credit
If you're trying to send SMS messages to mobile phones, each text costs money. By purchasing Skype Credit, you are able to do so through Skype. If your account doesn't have sufficient funds, Skype won't send SMS texts. You'll need to purchase more Skype Credit.
The user you're trying to contact may not exist anymore. The account could have been temporarily or permanently banned. Or perhaps the user you're trying to message has blocked your account. There is no way to tell unless you make contact with that user outside of Skype.