Numerically Stable IIR filter
First of all, what is the order of your IIR filter? The highest order I have ever used was an order-10 IIR filter for a control loop application. I feel like it is unlikely that you need more that this.

Second, it is a good idea to split your filter in second-order-sections (SOS) and cascade them , this usually fix most issues. 

https://www.dsprelated.com/showarticle/1137.php

You can also split your filter in second-order-sections and put them in parallel and add their ouputs too.