Pollution experts trying to remove cargo from the RMS Mulheim say they will now have to get rid of the platform rig set up alongside the vessel.
About 100 tonnes of cargo were being removed each day
The weather stopped the salvage operation on Wednesday, and the Maritime and Coastguard Agency (MCA) says sea conditions are getting worse.
It is feared the rig could also end up on rocks unless it is moved.
Salvors will return to a conveyor belt method to remove the shredded plastic, but that will not be as fast.
The RMS Mulheim ran aground between Sennen and Land's End more than two weeks ago.
But rough seas have continually hampered efforts to clear cargo.
A two-tonne grab claw on the rig and other equipment have already been washed into the sea,.
An MCA spokeswoman said: "The operation with the rig was always a risky one relying on a window of good weather."
"Unpredicted levels of sea swell have put a stop to that."
The Mulheim was carrying 2,200 tonnes of cargo when she ran aground between Sennen and Land's End on March 22.
The removal equipment is to be inspected for damage and the vessel's remaining cargo is to be cleared via a mechanised conveyor system when weather permits.
Up to half the Mulheim's cargo has already fallen into the sea.
Local authorities are carrying out daily inspections of nearby beaches for washed up plastic.
So far only a small amount has been recovered.
The vessel's fate will be decided after her cargo has been cleared.
She was en route from Cork to Lubeck, Germany, when she ran aground.
Her cargo of shredded plastic was destined for a landfill site.