I got the same referee report from two different journals My coauthor and I submitted our article for publication to one of the best journals in our field. After a long time of review, we got a rejection decision by the editor based on the referee report which we received. After that we wrote to the editor and explained to him/her that the referee arguments to reject our paper are wrong and provided point by point evidence to support our conclusions. 

However, the editor did not accept our arguments so we then sent our paper to another journal which is also among the best in our field. After waiting for considerable time, we got a rejection decision from the second journal and the same referee report as the first journal. I repeat the two reports which we received from two journals are completely identical! We have asked the editor of the second journal for explanations why we got the same report and so far we have not heard any reply. 

Based on these facts, we believe that our paper is being rejected for some unknown personal reasons not clear to us rather than objective reasons connected with our work.  In between the two submissions, we have revised our paper based on the first journal referee report. 

Have your ever experienced such a situation? 

How should we behave in this case?

UPDATE: 

Based on some comments below about this post, I want to express my opinion in more details about this issue. I am an expert in my working field and have reviewed several papers too. However, if somebody is asked to review the same paper more than once from two different journals, it is ethical that the referee rejects to review the paper and gives the possibility to another referee to do it. The referee can have an option to explain to the second journal editor the reasons why he/she rejected the paper initially and also point out the comments which he/she received back from the authors through the first journal (as in our case) that his/her conclusions might be wrong.
As a reviewer, when I get asked to review a paper the second time I will see whether my comments from the initial review were addressed. If not, then I will submit the same review. Why should I update my review if the paper has not been updated?

Getting the same reviewer is a very common occurrence. Perhaps in your situation the reviewer is misguided. However, when re-submitting a paper you should make every effort to address previous reviews.  And, in any case, legitimate issues raised by the reviewer should be addressed. Even if you think the reviewer is confused, you should seek to clarify the confusing points. They may be confusing to others too.

In your position there is probably not much you can do other than write to the editor explaining the situation. The best argument you can put forth is to explain that all of the points in the review have already been addressed in the submission. That makes it look like the reviewer didn't read it, which means the editor may side with you.