Work began last September to re-model the road near the Posthouse roundabout and the Â£5.3m overhaul was due to be completed by March.
But the Highways Agency said work would now finish on 10 May, blaming drainage and bridge strengthening problems.
Wrexham MP Ian Lucas said the road works have caused major disruption.
He said: "While it was inevitable that some delays will occur when a large project like this is carried out, I do think that there have been real problems with the way these works have been managed."
Last month, the agency said a 24hour a day operation was under way to complete the road by March.
But it has now admitted the deadline will not be met.
"We are sorry about the delay to the completion of the scheme and we understand the frustrations felt by drivers experiencing delays at the junction," a  Highways Agency spokesman said.
"We will continue to work closely with our contractors to minimise the impact on road users in the area."
Road works between the A55 and A483 on the Chester-Wrexham border will take almost six weeks longer than expected to complete.