Opening an EPS in Corel X4

Good day

I have a CorelDraw X4, but do my design in Illustrator.

My one sign printed can only open and work with Corel.
However, when I open my latest designed EPS in Corel, a lot of detail is lost - some places where the lines of the drawing overlap, the colour disappears - and it goes transparent.

Any tips on how I can solve this - on a very tight deadline, and have not had this complications before...