First of all, thank you all for all the responses. I tried some different approach and finally, after a year of struggling found a solution. Sorry for not giving the HDD name. Here it is: WD750BPVT. I also didn't mention about second problem: the drive was clicking when idle, few times before disk spindown. I'll answer my own question to save hair on someone's head. The problem was not easy to track.
Writing a C# app was quite good approach, but it has its drawbacks. When I changed the code to write data instead of read, it was quite a success (none spindowns) but the drive was constantly clicking when idle (each 2-3 secs).
Someone would say, that the HDD is ready to die because of clicking sound and I should backup my data while getting ready to trash the device. However I found an explanation. The reason of all these things is a feature, designed to save some power and disk lifetime (sic!). This feature, or actually two of them are:
Automatic Acoustic Management (AAM)
Advanced Power Management (APM)
Power management regulates spindowns and acoustic management is responsible for head parking (clicking noise). All you have to do is simply disable both of these. You can do this for example in CrystalDiskInfo: functions -> advanced -> AAM/APM control, select the drive you want and click both disable buttons. Problem solved until reboot. Its not permanent, so adding CrystalDiskInfo to startup is a good move.
This solution might also work for other devices / manufacturers, so if you have similar problem I strongly suggest to try that out.