Firstly, my understanding of the interest elasticity of investment (IEI) is that it is the responsiveness of investment to changes in interest rates. As a result, I can think of one reason why the IEI may be affected: when there's a recession, the IEI may be more inelastic because of low business confidence and a negative accelerator effect. However, I believe there are most likely other fundamental factors that affects the IEI as well, which I haven't been able to think of.
Expected return on investments. If the expected return is much higher than interest rates, then elasticity will be low. When interest rates are close to the expected return elasticity will be high.
Money supply. When money is scarce the elasticity will be low. When money is abundant the elasticity will be high.