Sorry about that. I was [meaningful pause] delayed.
Well, I suppose I mis-spoke then. I have a great deal of her post-injury story thought out. How she loses the arm is not important to those subsequent events. I didn’t mean it would be insignificant in her development.
work calls, must go back 
Early in her career she was an ensign on a starship, who had the misfortune of accompanying the captain on an away mission.
She considers herself lucky that she only lost an arm![SIZE=3]O-kaaaay…it’s Labor Day, she’s having a cookout, & at the last moment before the guests arrive, she realizes she has no hamburger meat.
Thinking quickly, she seizes a cleaver & a food processor, & then…[/SIZE]
Clive Barker meets Martha Stewart?
Unfortunate run-in with a bunch of cube smugglers while on shore leave at Luna farside. (only refer to cube in the singular, in italics, but don’t explain what cube is or why people are smuggling it)
I am reminded of an actual incident encountered when I was in the military. Responded to a medical emergency – a crew member had hacked at his wrists (ineffectually, thank goodness). Before approaching the injured man, who was belligerently shouting at everyone to stay away, I asked what he’d cut himself with. The senior man told me that it was a box cutter. I asked where the box cutter was, and was told that they had taken it from him.
Thus assured that the injured man was unarmed, I approached him with calming words – only to have my sleeve ripped open by his box cutter!
I can imagine that in the future there would be tools with far more potential danger than a mere box cutter. Perhaps some sort of beam energy device for welding?
How about a freak “mailbox baseball” accident when she was a teenager. As if losing the arm weren’t bad enough, the government forced her to enlist because she was destroying mailboxes. (That’s a federal offense, right?)
Or you could just leave it as a mystery, but you could borrow a line from The Big Lebowski :
"YOU SEE WHAT HAPPENS?! THIS IS WHAT HAPPENS WHEN YOU FUCK A STRANGER IN THE ASS! "
she’s doing a load of laundry and opens the washer early and reaches in only to have the spinning fusion powered washing machine of the future pluck her arm off.
cancer
Ripped off when she was trying to squeeze through the subway doors during rush hour.
If you’re out of Threeks, you could always use a fork. 
Semi-seriously, tho, why not go with the ‘left it somewhere’ version of lost? Perhaps, in this distant future civilization, the removal of limbs is a common everyday occurance? Perhaps she just set it down somewhere one day and, like umbrellas, someone walked away with hers… now she walks lopsided, her own small arm offset by that of a OmegaWeightlifter from Perseid 8 who just happened to have keeled over that day, and since he’s not using his arm anymore…
Ok, right, that’s terrible. Don’t use that.
I’m gonna start my own story about it.
/me hums the tune to ‘Detachable Penis’
I love you guys, with your Rocky Horror & King Missile & that DORRANCE #5 HOOKS whats-her-name. When they separate the wheat from the chaff, you guys’ll definitely be the cream that rises to the top of the sheep at my fathers right hand.
She’s definitely going to lose it in combat (unless it’s a freak masturbation accident).
As a matter of fact I might tell it from her perspective. One minute she’s pinned down in a fire fight. The next she wakes up in the hospital. The viewer/reader will know as much as she does.
Hmmm…the idea has merit.
PS - did I mention you guys are awesome?
whoohooo!
But what if she wakes up in a hosptial and her charts and record read “FMA” which could be either Freak Masturbation Accident or Friendly Materials Accident - she was in combat and masturbating (or could have been) and rather than persue an inquiry that might be embarassing (or to put a blemish on her record by which she could be manipulated later) they put the catch all FMA on her records (even have their “numbers” interchangable so that it could be a ‘mistake’ and ‘corrected’ either way) and leave it hanging for a while, depending on how you need to do it.
Hell, give her a medal for it, too.
How about “used the wrong type of ammunition in a weapon”? Say, she accidentally loaded a 37mm grenade round designed for an automatic grenade launcher into a 37mm rifle-mounted grenade launcher, and the thing blew up when she pulled the trigger?