I have cordless blinds and rarely have had any issues and the issues I have had I was able to fix. I once read pull them straight out perpendicular to the window until you feel a pop and then it starts working normal again. I am not sure if that is what you meant by exercising the tension mechanism, but if not that has worked every time for me.
As for if it's the cordless blinds, I have $7 blinds from Menard's, so I am not talking expensive or nice by any means. I assume they are store brand, since they are 27x64 and only $7. 3 kids that kept destroying blinds for one reason or another, so I ended up going cheap and they are going 4 years strong.