I seemed to find solution: Add any Dynamic content into the field that gives you this problems, save the flow, and remove the Dynamic content by clicking on the cross next to it. This way the field is cleaned completely and will not wipe the existing records.
This worked for me.
You can double-check if you did it correctly, by selecting "Peek code" from the header of the flow step (three dots on the right side where the step name is. In the code you can see what will be updated (in my case, for all the fields that have been wiped out, the code was saying
"body": {
"Title": "",
"Request": "",
Where Title and Request were names of the fields which were being wiped. After I did the excercise described above, these lines from the code disappeared and the flow no more deleted the content of these two fields.
B.T.W If anyone knows how to edit this flow "code" directly, let me know, as this would be a huge help for me.
Thanks