Most sites move to https with few problems.
One possible problem area is redirecting the http version of the site to the https version of the site. If there are old redirects and all of them are not accounted for and redirected again properly then the link value into the historic URLs might not be passed on to the https version of the site. If your site had a lot of historic redirects, it might pay to have someone who knows a lot about htaccess take a look at how yours are being handled.
Another problem is when all of the possible URLs have not been addressed and some of these...
... are not being accommodated.
And, some folks have speculated that when a site goes from http to https that it receives a quality review and if it doesn't satisfy the review the traffic starts slowly slipping. I can't point to any references on this but I do know of sites that have been on a month-by-month traffic decline for six months to a year after converting to https.