Please suggest me what is the right or the most natural case of using phrases "due to technical reasons" and "for technical reasons"?
Why would you want to use 'due to' when 'for' works perfectly well?
@ivanleoncz correctly identifies such a usage with 'service providers' and gives an example from a bank. It is 'management-speak': language used, especially in corporate communications to make the writer sound more important (than they really are).
There is seldom, if ever, any good reason to prefer 'due to' when you could say 'for'.
I believe that it's a formal situation. So
due to seems more appropriate for such situation.
Service providers use this beginning of tense for notices of technical problems with their services.
Due to some technical issues, we are going to reschedule today's Google Hangout for the near future. We sincerely apologize for any inconvenience and will be posting updates here as to the new date and time for the Hangout. Please stay tuned!
Taken from this Facebook post from a bank.