My best bet is a mistake with the experimental design. You have As 3+ as your initial analyte however, your CV shows that your initial E = -1 V which means that your scan direction was towards positive potentials (from -1 V to 1 V). Are you trying to oxidize As further? My guess is that you were using the CV to locate the reduction potential and add an overpotential to be applied in the deposition step in the ASV. If the lower line of the CV is considered, then you almost have a current of zero at -0.4 V and -0.2 V, which are the potentials you used in the ASV and SWV respectively.

My advice is that (1) Use CV to locate the reduction potential of As. To do this, take a background scan first (in 1 M HCl) and then analyte scan (As + HCl). Start at a potential where there is zero current and sweep towards negative (reduction) potentials. The background scan will let you know what the H2 evolution potential on your WE is. (2) Once you find the potential where you suspect As to be reduced, add a few mV (overpotential), still within your solvent breakdown limit and use this potential as the deposition potential in the ASV.

Also, consider your working electrode (WE) and make sure it is stable within the potential window you are working in. Note that chloride oxidation is possible together with oxygen evolution on the positive side.

You don't mention your working electrode and its not clear what your solution concentration is. You should use a gold electrode to see As(III) by ASV. The peak for As(III)/As(0) should be around 0 V scanning positive from -0.4 V. If you use a gold wire electrode, then you can detect the As(III) in 0.1 M HCl or even pH between 1 and 2, so not very acidic. If you go more negative during deposition, i.e. -1 V, then you generate Cl2 and you oxidise all As(III) to As(V) and you detect it using the wire. if you are using a gold disk electrode you will have lost the signal altogether. perhaps that is what happened. Look for papers by Salaun and myself. I attach an example

Thank you very much for detailed description

I will follow suggestions to rule out my problem. 

Thank you professor C.M.G.Van den Berg for detailed information.

This is the latest publication related to Arsenic

I am also working on it.

You should increase deposition time, scan this parameter from 60 seconds to 360 seconds also do the same for deposition potential. During deposition manage to stir the system (Electrolyte + Analyte)

Dr Constant M. G. van den Berg , Thank you very much for the pdf document that you shared, finally after many months I was able to obtain reproducible peaks in my research!