How much is "still have supply"?
Might it be that they run out while moving, and the charge up with the solar panel after decloaking?
It should also be noted that normal warships still need cloaking equipment in order to successfully hide from prying eyes, even though the cloak button is enabled.
Also, other pirates can always see your civvie ships. You're not fooling *them* with the 'ol fake transponder and emissions signature... and all the criminals know your civilian pilot's license is a forgery
Oh, and also, ordering a fleet to cloak dosen't seem to work.
You have to order the individual ships to cloak before fleeting them.