Hello Michela,
Uneven sequencing is common on the Illumina platform. There are a few things you can do upstream in the sample preparation phase that should help with this. (Because this is a problem with sequencing, it's best to fix it before sequencing, instead of trying to deal with it downstream during analysis.)
The big thing my wet-lab colleagues did was normalize the amount of amplicon PCR product added to the Illumina sequencing run.
This is the basic workflow:
extract nucleotides -> PCR -> amplified libraries -> Illumina sequencing
They added a measurement and normalization step:
extract nucleotides -> PCR -> amplified libraries -> measure DNA concentration (Qubit, nanodrop, etc.) -> calculate needed volume to add a consistent mass of DNA -> Illumina
sequencing
Because the mass of PCR the product was more even, the reads per sample were more even. 
Let me know if this makes sense 
Are you and your team already doing something like this? If so, what concentrations of DNA are you measuring (ng/ml)?