Are Chebyshev Type 1 filters very unstable at very high orders? I am currently experimenting with a digital implementation of a Chebyshev Type 1 filter of mine, for audio purposes. I have written the code myself so I was wondering if the behavior I've noticed is due to bad code or something else. My implementation works perfectly fine up to an order of 30. I know that this is ridiculous but that's not the point, it's just for educational purposes.
Anyway, when using a filter of order 30 or higher part of the frequency response that should be flat has resonant peaks. For a lowpass filter, it meant boosted low frequencies for a highpass filter it resulted in boosted low-mids. The highpass filter did not behave this way when the cutoff was above the resonant peaks, by the way, and changing the ripple didn't change the trend.
Is this normal and a result of the filter getting more and more unstable? Or does this indicate that there is some part of the code not working properly?
I am using double precision where I can, but the framework I am working in wants the sample values with 32-bit precision so I can only do the filter coefficients and filter memory with 64-bit precision and have to reduce precision when writing to the audio buffer. Maybe that's an issue?

Edit: To add to my OP, I am using cascaded biquads to realize the filter.
With infinite-precision arithmetic they will be stable. However, since you don't have infinite-precision arithmetic, you will have quantization issues even if you use 64-bit precision. These quantization issues can make your filter unstable. Even if your filter is stable, perhaps you will not get the frequency response wanted because of these quantization issues.

First solution : split your order-30 IIR filter into 15 order-2 IIR filters and cascade them. This should fix your problem.

https://www.dsprelated.com/freebooks/filters/Series_Second_Order_Sections.html
https://www.mathworks.com/help/signal/ref/tf2sos.html

Alternatively : Instead of cascading, you can parallelize the order-2 IIR filters.

https://www.dsprelated.com/freebooks/filters/Parallel_First_and_or_Second_Order.html

Finally, do you really need an order-30 chebyshev filter? I find it hard to believe to you really more than an order-8 or order-10 IIR filter. 

Edit : You edited your post to mention that you already use biquads. Have you tried an simpler filter, like an order-4 IIR? Make sure it works for an order-4 IIR filter (i.e. 2 cascaded biquads) and then try increasing the order. Also, are you sure that your factorization algorithm is correct? Maybe, there's a simple bug hidden somewhere and it will be easier to spot it with a reduced-order filter.