I believe these can be safely ignored. Especially if you have Server.Address properly configured in your /etc/rstudio-connect/rstudio-connect.gcfg file, then this error is benign.
In fact, we issued a hotpatch to v1.8.2 that should have resolved this issue, as discussed here:
https://docs.rstudio.com/connect/news/
The other resource leak that was a part of the hot-patch is something that can cause Connect stability issues in your environment, so it would be worth looking at an upgrade as soon as you can! It should quiet these messages and provide a bit more stability to your server 
Thanks for reaching out and asking though!!