Like the Fluidic Tribble, the C-Store is the only way to (theoretically) get the Tribble of Borg, other than buying one that someone else has purchased from the C-Store and placed on the Exchange.
Sounds like you're experiencing the same bug that we're describing, and that has had a few short threads pop up since Free to Play hit and added this bug. You'd honestly think that Cryptic would want this one fixed, since it's costing them money...
Or this is a case of "working as intended" because we all know Tribble of Borg made everyone using it OP. Resistence is futile.
I actually do not leave mine equipped. Nanite Injectors, hypos, collective static grenades, and a cane are more useful. I use the ToB, then, should I die, fail to remember to use it again.