So, the activation of trial key is completed successfully.
Trial keys aren't activated. Only product keys can be activated. Trial extension keys are just a very simple way of giving your prospective customer a few more days to use your application.
Could you please help me and and advice why the following error is returned?
The most likely cause is this one customer modified (or tried to modify) your application. Tell them to uninstall then reinstall your app. The trial should then work.
Are there any known solutions of this problem?
We've fixed a great number of bugs since TA 2.13. The current version, as of me writing this, is 3.2. Get it on your API page.