I actually found a way around this.  You have to mark the project complete, and then click the "delete" button on the drop down arrow on the right.  It actually doesn't delete it, even though delete means to erase.  It archives/inactivates it.  Once you do this, you can inactivate your customer. 

If you ever have to reactivate, you cannot do it through the customers tab, though.  You first have to re-activate your customer.  Then you have to go to the projects tab, click the gear icon on the right and select "show deleted projects",  then change the status of your projects to "all statuses", and make sure it's showing you "all customers".  Then you can scroll through and find your project, and click the drop down arrow on the right and select "Undelete & whatever status you want (progress vs complete)".  Sometimes I've found a glitch and have trouble getting the project to reopen, but it doesn't happen too often.  Hope this helps.