I am using IE 11.0.1 on Windows Server 2012 R2 and have had no trouble creating links of any kind. Without having access to a system where the problem occurs, and without knowing exactly what is happening, I can't really help you. Apparently you are using the link tool to create your links and after you save your page the links either disappear altogether or the text is there but the texts do not behave as links.
You can create links manually. For instance, you can type the following into the editor:
[[start]]
[[http://example.com|Example]]
When you save these, they should be links:
start
Example
Can you do this?