Since you don't have timestamping enabled (right click on ftp session window and from the popup menu check "timestamps") it makes it very difficult to know how long the operation took before the connection was lost.
FlashFXP will wait a maximum of 5 minutes for a standard reply, if it doesn't receive one within that time the connection will be lost. Normally a rename (move) is instant, but it really depends on the ftp server and how it actually handles it.
I believe increasing the "connect timeout" in the preferences also increases this value
Preferences > Connection
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