Hi Valentinas,
Thank you for your question. Here is some advice that I believe could solve your problem.
Root Cause:
The cause is that Online Editor uses HTTP calls that contain the word multiterm in them and these are caught by a Rewrite Rule made for MultiTerm Online.
By default MultiTerm Online is running on port 8080 under Apache Tomcat.
In some environments the configuration is changed in order to run MultiTerm Online under port 80.
That means instead of accessing MultiTerm Online via
yourservername:8080/multiterm
you access MultiTerm Online in the browser with a url like the one below
yourservername/multiterm
In order to achieve this you have to configure a redirect in Apache Tomcat to port 80.
Additionally, you need to add a rewrite rule in your IIS.
The additional rewrite rule can have a higher priority than the rule that you have in IIS for the default multiterm api rewrite rule that is used by the Online Editor for termbase lookups.
Resolution:
This means that at the top level in IIS in the ReWrite rules section, you will see a rule like the last one at the bottom in the image below.
Note that there is another rule for multiterm api requests that is higher up - this one is used for the Online Editor as mentioned above.
The MultiTerm Online redirect rule though catches all requests that have 'multiterm' in it - due to the wildcard.
This rule MUST be the last one in that list, otherwise, it will match requests that should not be matched, the ones for term recognition in Online Editor.

Hope this helps.
Regards,
Gareth Anderson