Looking to see if anyone else has experienced similar issues. This has happened to me for quite some time - over a year, but I've been too lazy to report it.
Basically, it seems that after an extended period of time (several days) the RoyalTS app window becomes almost unusable. Moving the RoyalTS main window around the monitor or between monitors is very slow. I will click to drag the main window around and it takes 5-7 seconds before the screen follows. Also, moving between connections/tab in the interface is extremely slow. After clicking a tab it takes 3 - 4 seconds before the screen changes and the tab will accept input. I predominantly use RDP to 7-10 servers as a time and those connections might remain open for days.
Closing/reopening RoyalTS will resolve the issue.
I have to admit that my instance doesn't run longer than a day or two but I haven't seen this myself. Can you provide some numbers from the task manager (memory usage / private bytes) when you started Royal TS and the same when it becomes laggy? Maybe there's a memory leak which causes the slowdown.