Often a peptide chain in a model, and sometimes in reality, is broken. Residue 123 might directly follow residue 120 in the coordinate file without a peptide bond connecting the two. Usually, in PDB, Diamond, and DSN2 formats, it is implicitly assumed that each residue is linked to the next. When this does not happen Convert will err and link them. When you are first creating a sequence file you should be aware of the breaks in the main chain of your model and edit the sequence file to include this information.
Non-TNT formats do not include ability to define other kinds of links between residues. If you have non-standard crosslinks in your molecule you will have to edit the sequence file for these as well.