I suggest trying the following within your Teamspeak 3 Client;
- Open up your Teamspeak 3 Settings
- Head down to the 'Capture' tab
- Cycle through a number of your possible 'Capture Devices'
- Upon selecting a new 'Capture Device' press the 'Begin Test' button within the tab - Check if your microphone is working as expected. In the case it works as expected, save the settings.
- If the settings are still not working as you expected, try another capture device. If none are found working, check your microphone is not currently in use within another Application, as this may cause it to cut in and out between the two.
I cannot promise these steps will work, yet it is worth a try.