Ideas
Not only Recon's UAV, but all classes have this ability bug (since 18th of November or so). This ability bug is also not the only thing broken with training specializations (or whatever these are called what you level up in a match with experience):
1) Experience values and progress is very bugged. Sometimes you get the last perk/ability unlocked almost immediately after joining a game. I have unlocked ability with only < 300 experience points multiple times.
2) UI/HUD keeps spamming that you have unlocked some of these perks.
3) Activable ability cooldown/refresh rate is totally broken (like you reported). For example you can have over 100% uptime with UAV, Rally Squad, Thermal Overdrive or Restock Allies. Par this is very broken for game balancing sake, it is especially annoying with spamming Assault's Rally Squad with effect and voice line.
This has been driving me crazy for past two weeks.