This happened to me too. Although it wasn't Klingons i was fighting. Can't remember the race right now but definately wasn't Klingons. I tried using the /killme command twice. After approx 2-3 minutes, the respawn button reappeared and respawned me just fine.
I don't think I hit the ESC button repeatedly, but it was definitely more than 5 minutes before I gave up (the deep space encounter finished and the 5:00 countdown for a new one also finished) with no sign of a new respawn button.
Thanks for the tip, if/when it happens again I'll give the ESC a try