Sometimes freestyle renders will have gaps in the lines:
What causes this and how can I prevent it?
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Try the following:
A detailed explanation of these settings can be found here.
It is mainly caused by toggling "Chaining" feature in the Freestyle Lining Style panel, if you are sure it's not caused by any Freestyle modifiers.
If so, to prevent that, you may simply toggle "Enable Chaining" off, or just include "Contour" by toggling it in the Edge Types list. (But make sure "Same Object" is not toggled, which is right below the "Enable Chaining" checkbox.)
Note: this might still not be enough, you might be forced to apply "Smooth" Faces in Edit mode (press TAB in 3D View to switch) in the Shading/UVs sidebar (press T to open).
Since this might screw up the rendering of the model, you might want to duplicate the model and render the copy on another layer.