I am using a basic version of LinkedIn. I have been using Jetpack for about 6 months. I have had to reconnect Facebook in the past, but have successfully done that...in the past. I use the LinkedIn profile in Publicize to forward my blog posts to my Facebook and LinkedIn accounts. Some posts I choose not to forward to LinkedIn, so I will uncheck the LinkedIn option at times. This has worked fine until I recently upgraded to the new WordPress and the new Jetpack...on the same day. The next time a posted on my blog I wanted the post to go to both LinkedIn and Facebook, so I left both options checked on the post. Later...after not seeing the post forwarded, I went back into the post and saw a note on the page asking me to reconnect LinkedIn. I have not been able to successfully do that. The Facebook link says it is connected, but it has not forwarded the post, either. So it seems to be broken, also.
Does this help?