Keynes showed that savers and investors are separate groups which do not necessarily interact: financial intermediaries (banks) are in between. When a recession is present, investment may not be equal to saving because, although the interest rate is very low, 1) borrowers have poor sales prospect, 2) banks are afraid of lending because of potential bankruptcy, and 3) savers want to wait for higher returns. This causes a liquidity trap: some saving is idle.
Banks do tend to be very prudent when making loans to businesses when economic conditions do not seem promising. But, their reluctance to make loans is itself contributing to the economic slow down.