I tried this out and it works. I normally update my sitemap and resubmit it to google every day along with fresh content every day. I stopped submitting the sitemap for 3 days to see what would happen. Traffic dropped by about 100+ visitors from google each day. I then resubmitted the sitemap and pinged google. Traffic came back. Give this a shot on your sites and see how it goes.
There is no need to submit your sitemap so frequently. That is a big waste of time. A website can get great rankings & traffic without ever submitting a sitemap to any search engine. There may be other explanations for your drop in traffic. Since rankings depend on about 200 factors, changing one factor doesn't necessarily prove that this factor is causing a drop in traffic. Most websites would not get any kind of boost in traffic simply by submitting a sitemap more often.