My client has multiple Schedule C businesses, some of which lose money. The IRS is only using the positive income businesses and ignoring the losses from the others. Is this accurate?

Yes, generally the IRS position is that the businesses that are losing money can be closed or shut down, and so allowing those losses against the actual income of the taxpayer is inappropriate. The taxpayer should effectively shut down the losing businesses instead of wasting income from the successful ones supporting them.
Sometimes taxpayers have multiple businesses but they are intertwined, such as a company that just manages the overhead and is separate from the operating company. This might be done for liability or other contractual reasons. In cases like this the taxpayer should either consider restructuring their operations so they are both under one company, or be able to show the IRS that the company that is losing money is required to do so and be active in order for the other company to succeed.