Yup we have a dehumidifier running constantly that drains into the sump pit. The basement still has a basement smell even though it's all brand new drywall, fresh paint, etc. The dehumidifier keeps the humidity around 40%, otherwise it would be approaching 75-80%
Do you know if there's an impermeable barrier on the interior walls? And what foundation material behind the drywall?
It gets dicey applying internal barriers, because one needs to be thoughtful about making sure there's a place for water to go when it's actually too much (you don't want an internal barrier to be a dam holding back all the pressure), but it can be an option.
They sell them in membrane form or paint-type form.
