Please check to see if the Method Integration Engine is up and running and your Quickbooks file is open. If the sync engine is working, the customer you are deleting may have transactions associated with it.
If customers have previous transactions, QuickBooks will not allow Method to delete them. If you check QuickBook -> Resolve Conflicts there may be a list of conflicts corresponding to the customers you tried to delete. From here you can click Delete From Method which will delete those customers from method but leave the customer and their transactions in QuickBooks. Alternatively, if you want to you can Refetch from QuickBooks which will keep the customer in Method, and from there you can simply rename the customer something else to keep it out of the way.
Sam