what you are describing can happen anytime for any antibody in any expression system. It is simply related to the folding efficiency and stability of the individual chains, i.e. heavy and light chain. In many cases the assembled Fab or full size antibody is more stable than the free chains, and you don't see much of the free (=unassembled) chains. However, in some cases one chain is unstable and then one observes (i) low levels of the assembled protein and (ii) excess of the other chain. You should analyze your VH sequence and check for problems (e.g. unusual amino acids at conserved positions). If problems persist you may consider to try a different expression system such as plants. Optimizing the expression in E.coli can take a lot of time and if the Fab doesn't behave well you'll get varying results. In the end a eukaryotic expression host may solve your problem by itself (i.e. host factors, chaperones). Plants are simple, cheap and rapid and Agro-infiltration would be my first choice.
All depends of course on your objectives, i.e what you want to use the Fab for.
Markus Sack Thank you very much for your valuable answer. I try to analyse the VH sequence as you suggested to understand the reason better, and the possibility to opt for other expression systems. Thank you very much :)