Look at the max timelines:
https://fred.stlouisfed.org/graph/?g=5f7L
https://fred.stlouisfed.org/series/DGS10
https://fred.stlouisfed.org/series/DGS30
It seems to me that inflation/deflation is not the motivating factor, but only the choice of risks. Where should one put gobs of money? Of course, the markets are an option, but the risks there seem terribly high. So, there is competition to put gobs of money in bonds, which drives rates down. People don't want low rate bonds, but those are the bonds that you get when they are in demand.
Even lower rates aren't going to drive cash into the markets and result in economic healing. They are only going to add more air to bubbles that already are making people wince in nervous expectation.