The Fair Debt Collection Act does not specify a maximum number of times, however it does say that the collector cannot repeatedly or continuously call with the intent to harass.
As per FDCPA (Federation of Debt Collections Practices Act), a bill collector can call you not more than once per day, unless you allow him or request him to call back at a later time. If a collector breaks the regulation, he can be penalized if complaint is lodged.
You can send a cease and desist letter to the credit card companies and they must then only contact you by mail. A bill collector hired by the credit company can call only once per day.
The answer to your question depends on the party to whom you owe the debt. Under the Fair Debt Collections Act, if the creditor has been hired by the original creditor they are allowed to call one time per day between the hours of 8am and 9pm. The original creditor does not have to follow this law, but most do.
People working for companies collecting money for bills believe that they are able to call any number of times per day until they reach somebody and get the bill resolved.