Thank you for your bug report.
I was able to reproduce the problem using the steps exactly as you described above.
This issue is caused by a recent change that eliminated a couple of steps and streamlined the rename operation. Prior to this change renaming a folder may have also required changing directories and refreshing the file listing from the server.
When these steps were eliminated it introduced an unforeseen issue where a variable used to hold the current working directory (relative to the server and case-insensitive) was no longer updated as part of the rename operation.
I have made a small change to the rename function so that this value is also updated.
This fix appears to solve the problem that you reported (based on my configuration), but additional testing is needed to ensure that this works in every situation and configuration.
You can download the updated build using the link below, unzip the flashfxp.exe into your FlashFXP program folder replacing the existing file.