The Futurama wikia mentions several reasons:
He is extremely poor and has stated several times that he has no home.
Hermes Conrad considers him as practically a slave. Everyone makes him
pay for stuff (even though he has no money and people will not pay him
any). A conversation Zoidberg has with the Professor suggests that he
is only staying with Planet Express because he is a slave, and must
"earn his freedom." (References to The Beast with a Billion Backs)
When Zoidberg recieved $300 from the mass tax refund, he thought he
To add on what Izkata, Zoidberg has no value for money. When Fry was a Holophoner musician, Zoidberg bought extra items on two occasions: Newspaper, and a 2-record set. Zoidberg also has bad credit(his credit card application was denied).
In another occasion, Fry and Bender flew the Planet Express Ship causing the entire Planet Express building to follow the ship cause major damage. Hermes then said that Zoidberg had to pay for the damages.
All in all, Zoidberg is the Millhouse of Futurama. He always gets picked on, and he's the type of character that wont improve in his situation.