If old saves are ok, and the behaviour is the same when you swap who is hosting, it probably isn't a conflict with a background program, etc.
If one of you joins in an old save, does loading a recent save after that cause a disconnection (immediately, or after a few minutes)?
Please email supportdos@larian.com, with a description of the problem and the report.zip file (or a Dropbox or Google drive link, etc) generated by the D:OS EE Analysis Tool (for Windows), for each of you. Extract the zip file somewhere and run AnalysisTool.exe. When that loads, browse to the install folder (if it is not automatically detected), optionally run the tests first, and then generate a report (it will be saved in the same location as the Analysis Tool).
The report will contain system and game information, as well as your saved games. To reduce the file size, one person can delete all their saves, while the other deletes most, just leaving the latest save, the most recent save where you can still connect fine and the oldest where you can not.
