working with IT Services firms

How does one deal with the large IT Services firms when they become very delinquent in paying invoices?
For many years I've only dealt direct with a customer.
Now working for a large firm. on 1099, have a contract (their contract)
for payment xx days after billing, regardless of whether they have been paid by end customer. But they are regularly 30 days beyond that.
I send reminders, called, and occassionally get a check, but never catch up.
Do I tell the customer?
Does it take having a lawyer?
In 25 years I've never walked out on a customer's project.
jim