It is difficult to know how your redirects have effected your site without getting into detail.
When redirecting an old site to a new site, I recommend a blanket redirect. Not doing this may not give you the effect you want.
From there, I then recommend doing page specific redirects on your new site to make corrections.
This method seems to work the best. It may not be too late to change your redirect methods and recapture rank/traffic.
Since it has been a year and you have not seen a rebound, I would be considering if inbound (back) links to the old site are important to retain. You may consider dropping the old link profile by deleting the old domain. Because there has been no recovery, it seems to me that this can be a viable option.
I would make sure that as much as you can, replacing the link profile to the old website with links to the new site before deleting the old site. I would skip the low values links and try and replicate valuable links or replace with links of relatively equal or better value. You can do this fairly quickly if you are not too hung-up on lower value links and are able to capture new links of value. It may be that your new site already has a link profile that trumps losing links from the old site.
This a personal decision you have to make after reviewing the link profiles of both sites.
But then again, sometimes it is best to cut bait and fish- meaning you may be better of cutting your loses and moving on. This is something only you can decide.